LMFDB - Group of Dirichlet characters of modulus 1800

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1800)

pari: g = idealstar(,1800,2)

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	=	$\chi_{1800}(1351,\cdot)$, $\chi_{1800}(901,\cdot)$, $\chi_{1800}(1001,\cdot)$, $\chi_{1800}(577,\cdot)$

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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{1800}(1,\cdot)$	1800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1800}(7,\cdot)$	1800.cl	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{1800}(11,\cdot)$	1800.dd	30	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{1800}(13,\cdot)$	1800.dl	60	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{1800}(17,\cdot)$	1800.ct	20	no	$1$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{1800}(19,\cdot)$	1800.bx	10	no	$-1$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1800}(23,\cdot)$	1800.dp	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1800}(29,\cdot)$	1800.di	30	yes	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1800}(31,\cdot)$	1800.de	30	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1800}(37,\cdot)$	1800.cr	20	no	$-1$	$1$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1800}(41,\cdot)$	1800.cy	30	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1800}(43,\cdot)$	1800.ce	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{1800}(47,\cdot)$	1800.dp	60	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1800}(49,\cdot)$	1800.bj	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{1800}(53,\cdot)$	1800.co	20	no	$1$	$1$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1800}(59,\cdot)$	1800.cx	30	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1800}(61,\cdot)$	1800.cv	30	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1800}(67,\cdot)$	1800.dr	60	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{1800}(71,\cdot)$	1800.bq	10	no	$1$	$1$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{1800}(73,\cdot)$	1800.cq	20	no	$-1$	$1$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{1800}(77,\cdot)$	1800.do	60	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1800}(79,\cdot)$	1800.cw	30	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1800}(83,\cdot)$	1800.dm	60	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{1800}(89,\cdot)$	1800.bv	10	no	$-1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1800}(91,\cdot)$	1800.br	10	no	$-1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1800}(97,\cdot)$	1800.dq	60	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{1800}(101,\cdot)$	1800.bb	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{1800}(103,\cdot)$	1800.dk	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{1800}(107,\cdot)$	1800.r	4	no	$-1$	$1$	$-i$	$-1$	$i$	$-i$	$-1$	$-i$	$-1$	$-1$	$-i$	$-1$
$\chi_{1800}(109,\cdot)$	1800.bu	10	no	$1$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1800}(113,\cdot)$	1800.dn	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{1800}(119,\cdot)$	1800.cz	30	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$

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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 $\F_{q}$

Modulus	$1800$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order	$480$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1800}(1,\cdot)\)	1800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1800}(7,\cdot)\)	1800.cl	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1800}(11,\cdot)\)	1800.dd	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{1800}(13,\cdot)\)	1800.dl	60	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{1800}(17,\cdot)\)	1800.ct	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{1800}(19,\cdot)\)	1800.bx	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1800}(23,\cdot)\)	1800.dp	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1800}(29,\cdot)\)	1800.di	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1800}(31,\cdot)\)	1800.de	30	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1800}(37,\cdot)\)	1800.cr	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1800}(41,\cdot)\)	1800.cy	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1800}(43,\cdot)\)	1800.ce	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1800}(47,\cdot)\)	1800.dp	60	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1800}(49,\cdot)\)	1800.bj	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1800}(53,\cdot)\)	1800.co	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1800}(59,\cdot)\)	1800.cx	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1800}(61,\cdot)\)	1800.cv	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1800}(67,\cdot)\)	1800.dr	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{1800}(71,\cdot)\)	1800.bq	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{1800}(73,\cdot)\)	1800.cq	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{1800}(77,\cdot)\)	1800.do	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1800}(79,\cdot)\)	1800.cw	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1800}(83,\cdot)\)	1800.dm	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{1800}(89,\cdot)\)	1800.bv	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1800}(91,\cdot)\)	1800.br	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1800}(97,\cdot)\)	1800.dq	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{1800}(101,\cdot)\)	1800.bb	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1800}(103,\cdot)\)	1800.dk	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{1800}(107,\cdot)\)	1800.r	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{1800}(109,\cdot)\)	1800.bu	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1800}(113,\cdot)\)	1800.dn	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{1800}(119,\cdot)\)	1800.cz	30	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)

Introduction

L-functions

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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.