LMFDB - Group of Dirichlet characters of modulus 9900

sage:H = DirichletGroup(9900)

pari:g = idealstar(,9900,2)

Character group

sage:G.order() pari:g.no
Order	=	2400
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{10}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{9900}(4951,\cdot)$, $\chi_{9900}(5501,\cdot)$, $\chi_{9900}(2377,\cdot)$, $\chi_{9900}(4501,\cdot)$

First 32 of 2400 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{9900}(1,\cdot)$	9900.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9900}(7,\cdot)$	9900.mm	60	no	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{9900}(13,\cdot)$	9900.lx	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{49}{60}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$-i$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{9900}(17,\cdot)$	9900.gk	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$
$\chi_{9900}(19,\cdot)$	9900.ds	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$
$\chi_{9900}(23,\cdot)$	9900.lu	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{9900}(29,\cdot)$	9900.kn	30	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9900}(31,\cdot)$	9900.it	30	yes	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9900}(37,\cdot)$	9900.hg	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$
$\chi_{9900}(41,\cdot)$	9900.id	30	no	$1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9900}(43,\cdot)$	9900.fh	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{9900}(47,\cdot)$	9900.lt	60	yes	$-1$	$1$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{60}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{30}\right)$	$i$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{9900}(49,\cdot)$	9900.il	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{9900}(53,\cdot)$	9900.gv	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{9900}(59,\cdot)$	9900.kr	30	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{9900}(61,\cdot)$	9900.ic	30	no	$-1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$-1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9900}(67,\cdot)$	9900.lk	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{9900}(71,\cdot)$	9900.dx	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-1$
$\chi_{9900}(73,\cdot)$	9900.ho	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{9900}(79,\cdot)$	9900.hx	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9900}(83,\cdot)$	9900.mc	60	yes	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{9900}(89,\cdot)$	9900.by	10	no	$-1$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{9900}(91,\cdot)$	9900.dr	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{9900}(97,\cdot)$	9900.mf	60	no	$-1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{9900}(101,\cdot)$	9900.ih	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{9900}(103,\cdot)$	9900.lp	60	yes	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{9900}(107,\cdot)$	9900.hk	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$
$\chi_{9900}(109,\cdot)$	9900.ez	10	no	$-1$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$1$
$\chi_{9900}(113,\cdot)$	9900.ld	60	no	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{9900}(119,\cdot)$	9900.jq	30	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{9900}(127,\cdot)$	9900.ha	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{9900}(131,\cdot)$	9900.hq	30	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$

Click here to search among the remaining 2368 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 $\F_{q}$
Belyi maps

Modulus	$9900$
Structure	\(C_{2}\times C_{2}\times C_{10}\times C_{60}\)
Order	$2400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{9900}(1,\cdot)\)	9900.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9900}(7,\cdot)\)	9900.mm	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{9900}(13,\cdot)\)	9900.lx	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(-i\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{9900}(17,\cdot)\)	9900.gk	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)
\(\chi_{9900}(19,\cdot)\)	9900.ds	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(-1\)
\(\chi_{9900}(23,\cdot)\)	9900.lu	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{9900}(29,\cdot)\)	9900.kn	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9900}(31,\cdot)\)	9900.it	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(37,\cdot)\)	9900.hg	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)
\(\chi_{9900}(41,\cdot)\)	9900.id	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(43,\cdot)\)	9900.fh	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{9900}(47,\cdot)\)	9900.lt	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(i\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{9900}(49,\cdot)\)	9900.il	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{9900}(53,\cdot)\)	9900.gv	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)
\(\chi_{9900}(59,\cdot)\)	9900.kr	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{9900}(61,\cdot)\)	9900.ic	30	no	\(-1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(-1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(67,\cdot)\)	9900.lk	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{9900}(71,\cdot)\)	9900.dx	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)
\(\chi_{9900}(73,\cdot)\)	9900.ho	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{9900}(79,\cdot)\)	9900.hx	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(83,\cdot)\)	9900.mc	60	yes	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{9900}(89,\cdot)\)	9900.by	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{9900}(91,\cdot)\)	9900.dr	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{9900}(97,\cdot)\)	9900.mf	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{9900}(101,\cdot)\)	9900.ih	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{9900}(103,\cdot)\)	9900.lp	60	yes	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{9900}(107,\cdot)\)	9900.hk	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)
\(\chi_{9900}(109,\cdot)\)	9900.ez	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)
\(\chi_{9900}(113,\cdot)\)	9900.ld	60	no	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{9900}(119,\cdot)\)	9900.jq	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{9900}(127,\cdot)\)	9900.ha	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{9900}(131,\cdot)\)	9900.hq	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 2400 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.