LMFDB - Group of Dirichlet characters of modulus 900

Show commands: PariGP / SageMath

sage: H = DirichletGroup(900)

pari: g = idealstar(,900,2)

Character group

sage: G.order() pari: g.no
Order	=	240
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{900}(451,\cdot)$, $\chi_{900}(101,\cdot)$, $\chi_{900}(577,\cdot)$

First 32 of 240 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{900}(1,\cdot)$	900.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{900}(7,\cdot)$	900.bf	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{900}(11,\cdot)$	900.br	30	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{900}(13,\cdot)$	900.bv	60	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{15}\right)$
$\chi_{900}(17,\cdot)$	900.bk	20	no	$1$	$1$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{900}(19,\cdot)$	900.bb	10	no	$-1$	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{900}(23,\cdot)$	900.bu	60	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{900}(29,\cdot)$	900.bo	30	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{900}(31,\cdot)$	900.bp	30	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{900}(37,\cdot)$	900.bi	20	no	$-1$	$1$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{900}(41,\cdot)$	900.bm	30	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{900}(43,\cdot)$	900.bf	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$
$\chi_{900}(47,\cdot)$	900.bu	60	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{900}(49,\cdot)$	900.s	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{900}(53,\cdot)$	900.bk	20	no	$1$	$1$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{900}(59,\cdot)$	900.bn	30	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{900}(61,\cdot)$	900.bg	15	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{900}(67,\cdot)$	900.bs	60	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{900}(71,\cdot)$	900.v	10	no	$1$	$1$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{900}(73,\cdot)$	900.bi	20	no	$-1$	$1$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{900}(77,\cdot)$	900.bt	60	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{900}(79,\cdot)$	900.bl	30	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{900}(83,\cdot)$	900.bu	60	yes	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{900}(89,\cdot)$	900.y	10	no	$-1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{900}(91,\cdot)$	900.x	10	no	$-1$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{900}(97,\cdot)$	900.bv	60	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{900}(101,\cdot)$	900.p	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{900}(103,\cdot)$	900.bs	60	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{900}(107,\cdot)$	900.m	4	no	$-1$	$1$	$-i$	$1$	$-i$	$-i$	$1$	$-i$	$1$	$-1$	$i$	$-1$
$\chi_{900}(109,\cdot)$	900.w	10	no	$1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{900}(113,\cdot)$	900.bt	60	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{900}(119,\cdot)$	900.bn	30	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$

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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	$900$
Structure	\(C_{2}\times C_{2}\times C_{60}\)
Order	$240$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{900}(1,\cdot)\)	900.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{900}(7,\cdot)\)	900.bf	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{900}(11,\cdot)\)	900.br	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{900}(13,\cdot)\)	900.bv	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)
\(\chi_{900}(17,\cdot)\)	900.bk	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{900}(19,\cdot)\)	900.bb	10	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{900}(23,\cdot)\)	900.bu	60	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{900}(29,\cdot)\)	900.bo	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{900}(31,\cdot)\)	900.bp	30	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{900}(37,\cdot)\)	900.bi	20	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{900}(41,\cdot)\)	900.bm	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{900}(43,\cdot)\)	900.bf	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{900}(47,\cdot)\)	900.bu	60	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{900}(49,\cdot)\)	900.s	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{900}(53,\cdot)\)	900.bk	20	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{900}(59,\cdot)\)	900.bn	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{900}(61,\cdot)\)	900.bg	15	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{900}(67,\cdot)\)	900.bs	60	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{900}(71,\cdot)\)	900.v	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{900}(73,\cdot)\)	900.bi	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{900}(77,\cdot)\)	900.bt	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{900}(79,\cdot)\)	900.bl	30	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{900}(83,\cdot)\)	900.bu	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{900}(89,\cdot)\)	900.y	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{900}(91,\cdot)\)	900.x	10	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{900}(97,\cdot)\)	900.bv	60	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{900}(101,\cdot)\)	900.p	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{900}(103,\cdot)\)	900.bs	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{900}(107,\cdot)\)	900.m	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{900}(109,\cdot)\)	900.w	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{900}(113,\cdot)\)	900.bt	60	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{900}(119,\cdot)\)	900.bn	30	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)

Introduction

L-functions

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Character group

First 32 of 240 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.