LMFDB - Group of Dirichlet characters of modulus 2100

sage:H = DirichletGroup(2100)

pari:g = idealstar(,2100,2)

Character group

sage:G.order() pari:g.no
Order	=	480
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2100}(1051,\cdot)$, $\chi_{2100}(701,\cdot)$, $\chi_{2100}(1177,\cdot)$, $\chi_{2100}(1501,\cdot)$

First 32 of 480 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	$-1$	$1$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{2100}(1,\cdot)$	2100.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2100}(11,\cdot)$	2100.dd	30	yes	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{2100}(13,\cdot)$	2100.co	20	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{2100}(17,\cdot)$	2100.dm	60	no	$-1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{2100}(19,\cdot)$	2100.cy	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{2100}(23,\cdot)$	2100.dq	60	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{2100}(29,\cdot)$	2100.ca	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$-1$
$\chi_{2100}(31,\cdot)$	2100.da	30	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{10}\right)$	$-1$
$\chi_{2100}(37,\cdot)$	2100.dp	60	no	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{4}{5}\right)$	$-i$
$\chi_{2100}(41,\cdot)$	2100.cb	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$
$\chi_{2100}(43,\cdot)$	2100.t	4	no	$1$	$1$	$-1$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$-i$	$1$	$-i$
$\chi_{2100}(47,\cdot)$	2100.do	60	yes	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{5}\right)$	$i$
$\chi_{2100}(53,\cdot)$	2100.dk	60	no	$1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{2100}(59,\cdot)$	2100.de	30	yes	$-1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$	$1$
$\chi_{2100}(61,\cdot)$	2100.dg	30	no	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{10}\right)$	$1$
$\chi_{2100}(67,\cdot)$	2100.dn	60	no	$1$	$1$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{5}\right)$	$i$
$\chi_{2100}(71,\cdot)$	2100.br	10	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$
$\chi_{2100}(73,\cdot)$	2100.dr	60	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$
$\chi_{2100}(79,\cdot)$	2100.cz	30	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{2100}(83,\cdot)$	2100.cp	20	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{2100}(89,\cdot)$	2100.cv	30	no	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{2100}(97,\cdot)$	2100.co	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{2100}(101,\cdot)$	2100.bi	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$
$\chi_{2100}(103,\cdot)$	2100.dl	60	no	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{10}\right)$	$-i$
$\chi_{2100}(107,\cdot)$	2100.cf	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$
$\chi_{2100}(109,\cdot)$	2100.dh	30	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{5}\right)$	$-1$
$\chi_{2100}(113,\cdot)$	2100.ct	20	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{2100}(121,\cdot)$	2100.cm	15	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{2100}(127,\cdot)$	2100.cs	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$
$\chi_{2100}(131,\cdot)$	2100.dj	30	yes	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$-1$
$\chi_{2100}(137,\cdot)$	2100.dk	60	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{2100}(139,\cdot)$	2100.bw	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$

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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	$2100$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{2100}(1,\cdot)\)	2100.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2100}(11,\cdot)\)	2100.dd	30	yes	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{2100}(13,\cdot)\)	2100.co	20	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)
\(\chi_{2100}(17,\cdot)\)	2100.dm	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{2100}(19,\cdot)\)	2100.cy	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{2100}(23,\cdot)\)	2100.dq	60	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)
\(\chi_{2100}(29,\cdot)\)	2100.ca	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)
\(\chi_{2100}(31,\cdot)\)	2100.da	30	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)
\(\chi_{2100}(37,\cdot)\)	2100.dp	60	no	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)
\(\chi_{2100}(41,\cdot)\)	2100.cb	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)
\(\chi_{2100}(43,\cdot)\)	2100.t	4	no	\(1\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)
\(\chi_{2100}(47,\cdot)\)	2100.do	60	yes	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)
\(\chi_{2100}(53,\cdot)\)	2100.dk	60	no	\(1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{2100}(59,\cdot)\)	2100.de	30	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)
\(\chi_{2100}(61,\cdot)\)	2100.dg	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)
\(\chi_{2100}(67,\cdot)\)	2100.dn	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)
\(\chi_{2100}(71,\cdot)\)	2100.br	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)
\(\chi_{2100}(73,\cdot)\)	2100.dr	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)
\(\chi_{2100}(79,\cdot)\)	2100.cz	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{2100}(83,\cdot)\)	2100.cp	20	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{2100}(89,\cdot)\)	2100.cv	30	no	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{2100}(97,\cdot)\)	2100.co	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{2100}(101,\cdot)\)	2100.bi	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)
\(\chi_{2100}(103,\cdot)\)	2100.dl	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)
\(\chi_{2100}(107,\cdot)\)	2100.cf	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{2100}(109,\cdot)\)	2100.dh	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)
\(\chi_{2100}(113,\cdot)\)	2100.ct	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)
\(\chi_{2100}(121,\cdot)\)	2100.cm	15	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{2100}(127,\cdot)\)	2100.cs	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)
\(\chi_{2100}(131,\cdot)\)	2100.dj	30	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)
\(\chi_{2100}(137,\cdot)\)	2100.dk	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{2100}(139,\cdot)\)	2100.bw	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

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Properties

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Character group

First 32 of 480 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.