LMFDB - Group of Dirichlet characters of modulus 205

Show commands: PariGP / SageMath

sage: H = DirichletGroup(205)

pari: g = idealstar(,205,2)

Character group

sage: G.order() pari: g.no
Order	=	160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{40}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{205}(42,\cdot)$, $\chi_{205}(6,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{205}(1,\cdot)$	205.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{205}(2,\cdot)$	205.t	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{205}(3,\cdot)$	205.l	8	yes	$1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{205}(4,\cdot)$	205.r	10	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{205}(6,\cdot)$	205.z	40	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$-i$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{205}(7,\cdot)$	205.y	40	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{5}\right)$	$-i$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{39}{40}\right)$
$\chi_{205}(8,\cdot)$	205.t	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{205}(9,\cdot)$	205.j	4	yes	$1$	$1$	$1$	$-i$	$1$	$-i$	$-i$	$1$	$-1$	$i$	$-i$	$-i$
$\chi_{205}(11,\cdot)$	205.z	40	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{205}(12,\cdot)$	205.y	40	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{205}(13,\cdot)$	205.bb	40	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{205}(14,\cdot)$	205.m	8	yes	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{205}(16,\cdot)$	205.k	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{205}(17,\cdot)$	205.bb	40	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{205}(18,\cdot)$	205.u	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{205}(19,\cdot)$	205.ba	40	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{205}(21,\cdot)$	205.x	20	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{205}(22,\cdot)$	205.bb	40	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{205}(23,\cdot)$	205.v	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$-i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{205}(24,\cdot)$	205.ba	40	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{205}(26,\cdot)$	205.z	40	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$-i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{205}(27,\cdot)$	205.l	8	yes	$1$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{205}(28,\cdot)$	205.bb	40	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{10}\right)$	$-i$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{205}(29,\cdot)$	205.ba	40	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{205}(31,\cdot)$	205.p	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{205}(32,\cdot)$	205.f	4	yes	$-1$	$1$	$-i$	$-1$	$-1$	$i$	$1$	$i$	$1$	$-i$	$1$	$-1$
$\chi_{205}(33,\cdot)$	205.w	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{205}(34,\cdot)$	205.ba	40	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{205}(36,\cdot)$	205.x	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{205}(37,\cdot)$	205.u	20	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{205}(38,\cdot)$	205.l	8	yes	$1$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{205}(39,\cdot)$	205.s	20	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$

Click here to search among the remaining 128 characters.

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	$205$
Structure	\(C_{4}\times C_{40}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{205}(1,\cdot)\)	205.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{205}(2,\cdot)\)	205.t	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{205}(3,\cdot)\)	205.l	8	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{205}(4,\cdot)\)	205.r	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{205}(6,\cdot)\)	205.z	40	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{205}(7,\cdot)\)	205.y	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)
\(\chi_{205}(8,\cdot)\)	205.t	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{205}(9,\cdot)\)	205.j	4	yes	\(1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-i\)
\(\chi_{205}(11,\cdot)\)	205.z	40	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{205}(12,\cdot)\)	205.y	40	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{205}(13,\cdot)\)	205.bb	40	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{205}(14,\cdot)\)	205.m	8	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{205}(16,\cdot)\)	205.k	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{205}(17,\cdot)\)	205.bb	40	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{205}(18,\cdot)\)	205.u	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{205}(19,\cdot)\)	205.ba	40	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{205}(21,\cdot)\)	205.x	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{205}(22,\cdot)\)	205.bb	40	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{205}(23,\cdot)\)	205.v	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{205}(24,\cdot)\)	205.ba	40	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{205}(26,\cdot)\)	205.z	40	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{205}(27,\cdot)\)	205.l	8	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{205}(28,\cdot)\)	205.bb	40	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{205}(29,\cdot)\)	205.ba	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{205}(31,\cdot)\)	205.p	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{205}(32,\cdot)\)	205.f	4	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-1\)
\(\chi_{205}(33,\cdot)\)	205.w	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{205}(34,\cdot)\)	205.ba	40	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{205}(36,\cdot)\)	205.x	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{205}(37,\cdot)\)	205.u	20	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{205}(38,\cdot)\)	205.l	8	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{205}(39,\cdot)\)	205.s	20	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

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.