LMFDB - Group of Dirichlet characters of modulus 2400

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2400)

pari: g = idealstar(,2400,2)

Character group

sage: G.order() pari: g.no
Order	=	640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{40}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2400}(1951,\cdot)$, $\chi_{2400}(901,\cdot)$, $\chi_{2400}(1601,\cdot)$, $\chi_{2400}(577,\cdot)$

First 32 of 640 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2400}(1,\cdot)$	2400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2400}(7,\cdot)$	2400.y	4	no	$1$	$1$	$i$	$-i$	$-1$	$i$	$-i$	$-i$	$i$	$-1$	$-1$	$-1$
$\chi_{2400}(11,\cdot)$	2400.dy	40	yes	$1$	$1$	$-i$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{2400}(13,\cdot)$	2400.du	40	no	$-1$	$1$	$-1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{2400}(17,\cdot)$	2400.cz	20	no	$1$	$1$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{2400}(19,\cdot)$	2400.dz	40	no	$-1$	$1$	$-i$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{2400}(23,\cdot)$	2400.di	20	no	$-1$	$1$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{2400}(29,\cdot)$	2400.eb	40	yes	$-1$	$1$	$i$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{2400}(31,\cdot)$	2400.cj	10	no	$-1$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{2400}(37,\cdot)$	2400.du	40	no	$-1$	$1$	$-1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{2400}(41,\cdot)$	2400.cw	20	no	$-1$	$1$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{2400}(43,\cdot)$	2400.bp	8	no	$1$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$
$\chi_{2400}(47,\cdot)$	2400.dn	20	no	$-1$	$1$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2400}(49,\cdot)$	2400.d	2	no	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$
$\chi_{2400}(53,\cdot)$	2400.eg	40	yes	$1$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{2400}(59,\cdot)$	2400.ed	40	yes	$1$	$1$	$i$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{2400}(61,\cdot)$	2400.ea	40	no	$1$	$1$	$-i$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{2400}(67,\cdot)$	2400.dv	40	no	$1$	$1$	$-1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{2400}(71,\cdot)$	2400.dr	20	no	$1$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{2400}(73,\cdot)$	2400.dh	20	no	$-1$	$1$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{2400}(77,\cdot)$	2400.eg	40	yes	$1$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{2400}(79,\cdot)$	2400.cn	10	no	$-1$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{2400}(83,\cdot)$	2400.eh	40	yes	$-1$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{2400}(89,\cdot)$	2400.dp	20	no	$-1$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{2400}(91,\cdot)$	2400.ec	40	no	$-1$	$1$	$-i$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{2400}(97,\cdot)$	2400.db	20	no	$-1$	$1$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{2400}(101,\cdot)$	2400.ca	8	no	$-1$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{2400}(103,\cdot)$	2400.df	20	no	$1$	$1$	$-i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{2400}(107,\cdot)$	2400.cb	8	no	$-1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$
$\chi_{2400}(109,\cdot)$	2400.dx	40	no	$1$	$1$	$i$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{2400}(113,\cdot)$	2400.cz	20	no	$1$	$1$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{2400}(119,\cdot)$	2400.cu	20	no	$1$	$1$	$-1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$

Click here to search among the remaining 608 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	$2400$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{40}\)
Order	$640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2400}(1,\cdot)\)	2400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2400}(7,\cdot)\)	2400.y	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{2400}(11,\cdot)\)	2400.dy	40	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{2400}(13,\cdot)\)	2400.du	40	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{2400}(17,\cdot)\)	2400.cz	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{2400}(19,\cdot)\)	2400.dz	40	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{2400}(23,\cdot)\)	2400.di	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{2400}(29,\cdot)\)	2400.eb	40	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{2400}(31,\cdot)\)	2400.cj	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{2400}(37,\cdot)\)	2400.du	40	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{2400}(41,\cdot)\)	2400.cw	20	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{2400}(43,\cdot)\)	2400.bp	8	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)
\(\chi_{2400}(47,\cdot)\)	2400.dn	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2400}(49,\cdot)\)	2400.d	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2400}(53,\cdot)\)	2400.eg	40	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{2400}(59,\cdot)\)	2400.ed	40	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{2400}(61,\cdot)\)	2400.ea	40	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{2400}(67,\cdot)\)	2400.dv	40	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{2400}(71,\cdot)\)	2400.dr	20	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{2400}(73,\cdot)\)	2400.dh	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2400}(77,\cdot)\)	2400.eg	40	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{2400}(79,\cdot)\)	2400.cn	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{2400}(83,\cdot)\)	2400.eh	40	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{2400}(89,\cdot)\)	2400.dp	20	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{2400}(91,\cdot)\)	2400.ec	40	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{2400}(97,\cdot)\)	2400.db	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{2400}(101,\cdot)\)	2400.ca	8	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{2400}(103,\cdot)\)	2400.df	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{2400}(107,\cdot)\)	2400.cb	8	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)
\(\chi_{2400}(109,\cdot)\)	2400.dx	40	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{2400}(113,\cdot)\)	2400.cz	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{2400}(119,\cdot)\)	2400.cu	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 640 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.