LMFDB - Group of Dirichlet characters of modulus 41

Show commands: PariGP / SageMath

sage: H = DirichletGroup(41)

pari: g = idealstar(,41,2)

Character group

sage: G.order() pari: g.no
Order	=	40
sage: H.invariants() pari: g.cyc
Structure	=	$C_{40}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{41}(6,\cdot)$

First 32 of 40 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{41}(1,\cdot)$	41.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{41}(2,\cdot)$	41.g	20	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{41}(3,\cdot)$	41.e	8	yes	$-1$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$i$	$1$	$e\left(\frac{1}{8}\right)$
$\chi_{41}(4,\cdot)$	41.f	10	yes	$1$	$1$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{41}(5,\cdot)$	41.g	20	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{41}(6,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{41}(7,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{41}(8,\cdot)$	41.g	20	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{41}(9,\cdot)$	41.c	4	yes	$1$	$1$	$-1$	$i$	$1$	$-1$	$-i$	$i$	$-1$	$-1$	$1$	$i$
$\chi_{41}(10,\cdot)$	41.d	5	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{41}(11,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{41}(12,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{41}(13,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{41}(14,\cdot)$	41.e	8	yes	$-1$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$1$	$e\left(\frac{7}{8}\right)$
$\chi_{41}(15,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{41}(16,\cdot)$	41.d	5	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{41}(17,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{41}(18,\cdot)$	41.d	5	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{41}(19,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{41}(20,\cdot)$	41.g	20	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{41}(21,\cdot)$	41.g	20	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{41}(22,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{41}(23,\cdot)$	41.f	10	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{41}(24,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{40}\right)$
$\chi_{41}(25,\cdot)$	41.f	10	yes	$1$	$1$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{41}(26,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$-i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{41}(27,\cdot)$	41.e	8	yes	$-1$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$-1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$-i$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{41}(28,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{41}(29,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{41}(30,\cdot)$	41.h	40	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{41}(31,\cdot)$	41.f	10	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{41}(32,\cdot)$	41.c	4	yes	$1$	$1$	$-1$	$-i$	$1$	$-1$	$i$	$-i$	$-1$	$-1$	$1$	$-i$

Click here to search among the remaining 8 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	$41$
Structure	\(C_{40}\)
Order	$40$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{41}(1,\cdot)\)	41.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{41}(2,\cdot)\)	41.g	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{41}(3,\cdot)\)	41.e	8	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(i\)	\(1\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{41}(4,\cdot)\)	41.f	10	yes	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{41}(5,\cdot)\)	41.g	20	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{41}(6,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{41}(7,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{41}(8,\cdot)\)	41.g	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{41}(9,\cdot)\)	41.c	4	yes	\(1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(1\)	\(i\)
\(\chi_{41}(10,\cdot)\)	41.d	5	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{41}(11,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{41}(12,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{41}(13,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{41}(14,\cdot)\)	41.e	8	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-i\)	\(1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{41}(15,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{41}(16,\cdot)\)	41.d	5	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{41}(17,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{41}(18,\cdot)\)	41.d	5	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{41}(19,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{41}(20,\cdot)\)	41.g	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{41}(21,\cdot)\)	41.g	20	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{41}(22,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{41}(23,\cdot)\)	41.f	10	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{41}(24,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)
\(\chi_{41}(25,\cdot)\)	41.f	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{41}(26,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{41}(27,\cdot)\)	41.e	8	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(-i\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{41}(28,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{41}(29,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{41}(30,\cdot)\)	41.h	40	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{41}(31,\cdot)\)	41.f	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{41}(32,\cdot)\)	41.c	4	yes	\(1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(-i\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 40 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.