LMFDB - Group of Dirichlet characters of modulus 220

Show commands: PariGP / SageMath

sage: H = DirichletGroup(220)

pari: g = idealstar(,220,2)

Character group

sage: G.order() pari: g.no
Order	=	80
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{20}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{220}(111,\cdot)$, $\chi_{220}(177,\cdot)$, $\chi_{220}(101,\cdot)$

First 32 of 80 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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{220}(1,\cdot)$	220.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{220}(3,\cdot)$	220.v	20	yes	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{220}(7,\cdot)$	220.w	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{220}(9,\cdot)$	220.t	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{220}(13,\cdot)$	220.u	20	no	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{220}(17,\cdot)$	220.u	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{220}(19,\cdot)$	220.o	10	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{220}(21,\cdot)$	220.f	2	no	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$
$\chi_{220}(23,\cdot)$	220.l	4	no	$1$	$1$	$-i$	$i$	$-1$	$i$	$-i$	$1$	$1$	$-i$	$i$	$-1$
$\chi_{220}(27,\cdot)$	220.v	20	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{220}(29,\cdot)$	220.q	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{220}(31,\cdot)$	220.s	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{220}(37,\cdot)$	220.x	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{220}(39,\cdot)$	220.o	10	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{220}(41,\cdot)$	220.p	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{220}(43,\cdot)$	220.i	4	yes	$-1$	$1$	$-i$	$-i$	$-1$	$-i$	$i$	$-1$	$-1$	$-i$	$i$	$1$
$\chi_{220}(47,\cdot)$	220.v	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{220}(49,\cdot)$	220.t	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{220}(51,\cdot)$	220.r	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{220}(53,\cdot)$	220.x	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{220}(57,\cdot)$	220.u	20	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{220}(59,\cdot)$	220.n	10	yes	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{220}(61,\cdot)$	220.p	10	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{220}(63,\cdot)$	220.w	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{220}(67,\cdot)$	220.l	4	no	$1$	$1$	$i$	$-i$	$-1$	$-i$	$i$	$1$	$1$	$i$	$-i$	$-1$
$\chi_{220}(69,\cdot)$	220.t	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{220}(71,\cdot)$	220.s	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{220}(73,\cdot)$	220.u	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{220}(79,\cdot)$	220.o	10	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{220}(81,\cdot)$	220.m	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{220}(83,\cdot)$	220.w	20	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{220}(87,\cdot)$	220.i	4	yes	$-1$	$1$	$i$	$i$	$-1$	$i$	$-i$	$-1$	$-1$	$i$	$-i$	$1$

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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 $\F_{q}$

Modulus	$220$
Structure	\(C_{2}\times C_{2}\times C_{20}\)
Order	$80$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{220}(1,\cdot)\)	220.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{220}(3,\cdot)\)	220.v	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{220}(7,\cdot)\)	220.w	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{220}(9,\cdot)\)	220.t	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{220}(13,\cdot)\)	220.u	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{220}(17,\cdot)\)	220.u	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{220}(19,\cdot)\)	220.o	10	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{220}(21,\cdot)\)	220.f	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{220}(23,\cdot)\)	220.l	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)
\(\chi_{220}(27,\cdot)\)	220.v	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{220}(29,\cdot)\)	220.q	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{220}(31,\cdot)\)	220.s	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{220}(37,\cdot)\)	220.x	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{220}(39,\cdot)\)	220.o	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{220}(41,\cdot)\)	220.p	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{220}(43,\cdot)\)	220.i	4	yes	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(1\)
\(\chi_{220}(47,\cdot)\)	220.v	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{220}(49,\cdot)\)	220.t	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{220}(51,\cdot)\)	220.r	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{220}(53,\cdot)\)	220.x	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{220}(57,\cdot)\)	220.u	20	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{220}(59,\cdot)\)	220.n	10	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{220}(61,\cdot)\)	220.p	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{220}(63,\cdot)\)	220.w	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{220}(67,\cdot)\)	220.l	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{220}(69,\cdot)\)	220.t	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{220}(71,\cdot)\)	220.s	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{220}(73,\cdot)\)	220.u	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{220}(79,\cdot)\)	220.o	10	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{220}(81,\cdot)\)	220.m	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{220}(83,\cdot)\)	220.w	20	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{220}(87,\cdot)\)	220.i	4	yes	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)

Introduction

L-functions

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Character group

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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.