LMFDB - Group of Dirichlet characters of modulus 820

sage:H = DirichletGroup(820)

pari:g = idealstar(,820,2)

Character group

sage:G.order() pari:g.no
Order	=	320
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{40}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{820}(411,\cdot)$, $\chi_{820}(657,\cdot)$, $\chi_{820}(621,\cdot)$

First 32 of 320 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{820}(1,\cdot)$	820.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{820}(3,\cdot)$	820.ba	8	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{1}{8}\right)$
$\chi_{820}(7,\cdot)$	820.bz	40	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{40}\right)$	$-i$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{820}(9,\cdot)$	820.n	4	no	$1$	$1$	$-i$	$-i$	$-1$	$i$	$-i$	$i$	$-i$	$-1$	$-1$	$i$
$\chi_{820}(11,\cdot)$	820.bw	40	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{40}\right)$	$i$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{820}(13,\cdot)$	820.ca	40	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{39}{40}\right)$	$-i$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{820}(17,\cdot)$	820.ca	40	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{40}\right)$	$i$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{820}(19,\cdot)$	820.cc	40	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{40}\right)$	$-i$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{820}(21,\cdot)$	820.bo	20	no	$1$	$1$	$i$	$e\left(\frac{13}{20}\right)$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{820}(23,\cdot)$	820.bm	20	yes	$1$	$1$	$i$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$-i$
$\chi_{820}(27,\cdot)$	820.ba	8	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{3}{8}\right)$
$\chi_{820}(29,\cdot)$	820.bx	40	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{40}\right)$	$i$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{820}(31,\cdot)$	820.bh	10	no	$-1$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$1$
$\chi_{820}(33,\cdot)$	820.bu	20	no	$-1$	$1$	$1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$1$
$\chi_{820}(37,\cdot)$	820.bn	20	no	$-1$	$1$	$-i$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$i$
$\chi_{820}(39,\cdot)$	820.bp	20	yes	$-1$	$1$	$i$	$e\left(\frac{17}{20}\right)$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-i$
$\chi_{820}(43,\cdot)$	820.bk	20	yes	$1$	$1$	$-1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$-1$
$\chi_{820}(47,\cdot)$	820.by	40	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{40}\right)$	$i$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{820}(49,\cdot)$	820.bq	20	no	$1$	$1$	$-i$	$e\left(\frac{11}{20}\right)$	$-1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{820}(51,\cdot)$	820.bf	10	no	$-1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{820}(53,\cdot)$	820.ca	40	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{40}\right)$	$-i$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{820}(57,\cdot)$	820.bn	20	no	$-1$	$1$	$-i$	$e\left(\frac{13}{20}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$i$
$\chi_{820}(59,\cdot)$	820.bj	10	yes	$-1$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{820}(61,\cdot)$	820.bo	20	no	$1$	$1$	$-i$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$i$
$\chi_{820}(63,\cdot)$	820.bz	40	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{21}{40}\right)$	$i$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{820}(67,\cdot)$	820.by	40	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{40}\right)$	$i$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{820}(69,\cdot)$	820.bx	40	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{40}\right)$	$i$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{820}(71,\cdot)$	820.bw	40	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{40}\right)$	$i$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{820}(73,\cdot)$	820.t	4	no	$-1$	$1$	$1$	$-1$	$1$	$-i$	$1$	$1$	$-i$	$-1$	$i$	$1$
$\chi_{820}(77,\cdot)$	820.bl	20	no	$-1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$-1$
$\chi_{820}(79,\cdot)$	820.w	8	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$-1$	$e\left(\frac{3}{8}\right)$
$\chi_{820}(81,\cdot)$	820.b	2	no	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$-1$

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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	$820$
Structure	\(C_{2}\times C_{4}\times C_{40}\)
Order	$320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{820}(1,\cdot)\)	820.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{820}(3,\cdot)\)	820.ba	8	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(7,\cdot)\)	820.bz	40	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(-i\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{820}(9,\cdot)\)	820.n	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)
\(\chi_{820}(11,\cdot)\)	820.bw	40	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(i\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(13,\cdot)\)	820.ca	40	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(-i\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{820}(17,\cdot)\)	820.ca	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(i\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(19,\cdot)\)	820.cc	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(-i\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(21,\cdot)\)	820.bo	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{820}(23,\cdot)\)	820.bm	20	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)
\(\chi_{820}(27,\cdot)\)	820.ba	8	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(29,\cdot)\)	820.bx	40	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(i\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(31,\cdot)\)	820.bh	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)
\(\chi_{820}(33,\cdot)\)	820.bu	20	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)
\(\chi_{820}(37,\cdot)\)	820.bn	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(i\)
\(\chi_{820}(39,\cdot)\)	820.bp	20	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)
\(\chi_{820}(43,\cdot)\)	820.bk	20	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)
\(\chi_{820}(47,\cdot)\)	820.by	40	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(i\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(49,\cdot)\)	820.bq	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)
\(\chi_{820}(51,\cdot)\)	820.bf	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{820}(53,\cdot)\)	820.ca	40	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(-i\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{820}(57,\cdot)\)	820.bn	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(i\)
\(\chi_{820}(59,\cdot)\)	820.bj	10	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{820}(61,\cdot)\)	820.bo	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)
\(\chi_{820}(63,\cdot)\)	820.bz	40	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(i\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(67,\cdot)\)	820.by	40	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(i\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(69,\cdot)\)	820.bx	40	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(i\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{820}(71,\cdot)\)	820.bw	40	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(i\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(73,\cdot)\)	820.t	4	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(1\)
\(\chi_{820}(77,\cdot)\)	820.bl	20	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)
\(\chi_{820}(79,\cdot)\)	820.w	8	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{820}(81,\cdot)\)	820.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)

Introduction

L-functions

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Character group

First 32 of 320 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.