LMFDB - Group of Dirichlet characters of modulus 1200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1200)

pari: g = idealstar(,1200,2)

Character group

sage: G.order() pari: g.no
Order	=	320
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{20}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1200}(751,\cdot)$, $\chi_{1200}(901,\cdot)$, $\chi_{1200}(401,\cdot)$, $\chi_{1200}(577,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{1200}(1,\cdot)$	1200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1200}(7,\cdot)$	1200.bh	4	no	$1$	$1$	$-i$	$1$	$i$	$i$	$-1$	$i$	$1$	$-1$	$-i$	$1$
$\chi_{1200}(11,\cdot)$	1200.db	20	yes	$1$	$1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1200}(13,\cdot)$	1200.cr	20	no	$-1$	$1$	$i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1200}(17,\cdot)$	1200.cw	20	no	$1$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1200}(19,\cdot)$	1200.ch	20	no	$-1$	$1$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1200}(23,\cdot)$	1200.cx	20	no	$-1$	$1$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1200}(29,\cdot)$	1200.cz	20	yes	$-1$	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1200}(31,\cdot)$	1200.bt	10	no	$-1$	$1$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1200}(37,\cdot)$	1200.cr	20	no	$-1$	$1$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1200}(41,\cdot)$	1200.bz	10	no	$-1$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1200}(43,\cdot)$	1200.bc	4	no	$1$	$1$	$-i$	$-i$	$1$	$-i$	$-i$	$i$	$i$	$-1$	$1$	$-1$
$\chi_{1200}(47,\cdot)$	1200.ci	20	no	$-1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1200}(49,\cdot)$	1200.f	2	no	$1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{1200}(53,\cdot)$	1200.cm	20	yes	$1$	$1$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1200}(59,\cdot)$	1200.ce	20	yes	$1$	$1$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1200}(61,\cdot)$	1200.cf	20	no	$1$	$1$	$-1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1200}(67,\cdot)$	1200.cp	20	no	$1$	$1$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1200}(71,\cdot)$	1200.bw	10	no	$1$	$1$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1200}(73,\cdot)$	1200.cu	20	no	$-1$	$1$	$-i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1200}(77,\cdot)$	1200.cm	20	yes	$1$	$1$	$-i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1200}(79,\cdot)$	1200.cd	10	no	$-1$	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1200}(83,\cdot)$	1200.cs	20	yes	$-1$	$1$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1200}(89,\cdot)$	1200.bp	10	no	$-1$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1200}(91,\cdot)$	1200.cy	20	no	$-1$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1200}(97,\cdot)$	1200.cl	20	no	$-1$	$1$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1200}(101,\cdot)$	1200.r	4	no	$-1$	$1$	$-1$	$-i$	$-i$	$-1$	$-i$	$1$	$i$	$1$	$i$	$1$
$\chi_{1200}(103,\cdot)$	1200.ck	20	no	$1$	$1$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1200}(107,\cdot)$	1200.z	4	no	$-1$	$1$	$i$	$i$	$-1$	$-i$	$-i$	$i$	$-i$	$-1$	$-1$	$1$
$\chi_{1200}(109,\cdot)$	1200.da	20	no	$1$	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1200}(113,\cdot)$	1200.cw	20	no	$1$	$1$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{1200}(119,\cdot)$	1200.ca	10	no	$1$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$

Click here to search among the remaining 288 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	$1200$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{20}\)
Order	$320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1200}(1,\cdot)\)	1200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1200}(7,\cdot)\)	1200.bh	4	no	\(1\)	\(1\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{1200}(11,\cdot)\)	1200.db	20	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1200}(13,\cdot)\)	1200.cr	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1200}(17,\cdot)\)	1200.cw	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1200}(19,\cdot)\)	1200.ch	20	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1200}(23,\cdot)\)	1200.cx	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1200}(29,\cdot)\)	1200.cz	20	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(31,\cdot)\)	1200.bt	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1200}(37,\cdot)\)	1200.cr	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1200}(41,\cdot)\)	1200.bz	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1200}(43,\cdot)\)	1200.bc	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{1200}(47,\cdot)\)	1200.ci	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1200}(49,\cdot)\)	1200.f	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{1200}(53,\cdot)\)	1200.cm	20	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(59,\cdot)\)	1200.ce	20	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1200}(61,\cdot)\)	1200.cf	20	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1200}(67,\cdot)\)	1200.cp	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1200}(71,\cdot)\)	1200.bw	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1200}(73,\cdot)\)	1200.cu	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1200}(77,\cdot)\)	1200.cm	20	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1200}(79,\cdot)\)	1200.cd	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(83,\cdot)\)	1200.cs	20	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1200}(89,\cdot)\)	1200.bp	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1200}(91,\cdot)\)	1200.cy	20	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1200}(97,\cdot)\)	1200.cl	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(101,\cdot)\)	1200.r	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(1\)
\(\chi_{1200}(103,\cdot)\)	1200.ck	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1200}(107,\cdot)\)	1200.z	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{1200}(109,\cdot)\)	1200.da	20	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1200}(113,\cdot)\)	1200.cw	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{1200}(119,\cdot)\)	1200.ca	10	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

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.