LMFDB - Group of Dirichlet characters of modulus 155

Show commands: PariGP / SageMath

sage: H = DirichletGroup(155)

pari: g = idealstar(,155,2)

Character group

sage: G.order() pari: g.no
Order	=	120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{155}(32,\cdot)$, $\chi_{155}(96,\cdot)$

First 32 of 120 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{155}(1,\cdot)$	155.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{155}(2,\cdot)$	155.s	20	yes	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{155}(3,\cdot)$	155.x	60	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{155}(4,\cdot)$	155.n	10	yes	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{155}(6,\cdot)$	155.k	6	no	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{155}(7,\cdot)$	155.w	60	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{155}(8,\cdot)$	155.s	20	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{155}(9,\cdot)$	155.u	30	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{155}(11,\cdot)$	155.t	30	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{30}\right)$
$\chi_{155}(12,\cdot)$	155.x	60	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{155}(13,\cdot)$	155.x	60	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{17}{60}\right)$
$\chi_{155}(14,\cdot)$	155.u	30	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{155}(16,\cdot)$	155.h	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{155}(17,\cdot)$	155.x	60	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{155}(18,\cdot)$	155.w	60	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{155}(19,\cdot)$	155.u	30	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{155}(21,\cdot)$	155.t	30	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{155}(22,\cdot)$	155.x	60	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{155}(23,\cdot)$	155.r	20	yes	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{155}(24,\cdot)$	155.v	30	yes	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{155}(26,\cdot)$	155.k	6	no	$-1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{155}(27,\cdot)$	155.r	20	yes	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{155}(28,\cdot)$	155.w	60	yes	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{155}(29,\cdot)$	155.m	10	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{155}(32,\cdot)$	155.g	4	no	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-i$	$-1$	$1$	$i$	$-i$
$\chi_{155}(33,\cdot)$	155.s	20	yes	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{155}(34,\cdot)$	155.v	30	yes	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{155}(36,\cdot)$	155.e	3	no	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{155}(37,\cdot)$	155.p	12	yes	$1$	$1$	$i$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{155}(38,\cdot)$	155.w	60	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{155}(39,\cdot)$	155.n	10	yes	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{155}(41,\cdot)$	155.q	15	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$

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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	$155$
Structure	\(C_{2}\times C_{60}\)
Order	$120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{155}(1,\cdot)\)	155.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{155}(2,\cdot)\)	155.s	20	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{155}(3,\cdot)\)	155.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{155}(4,\cdot)\)	155.n	10	yes	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{155}(6,\cdot)\)	155.k	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{155}(7,\cdot)\)	155.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{155}(8,\cdot)\)	155.s	20	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{155}(9,\cdot)\)	155.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{155}(11,\cdot)\)	155.t	30	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)
\(\chi_{155}(12,\cdot)\)	155.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{155}(13,\cdot)\)	155.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)
\(\chi_{155}(14,\cdot)\)	155.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{155}(16,\cdot)\)	155.h	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{155}(17,\cdot)\)	155.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{155}(18,\cdot)\)	155.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{155}(19,\cdot)\)	155.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{155}(21,\cdot)\)	155.t	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{155}(22,\cdot)\)	155.x	60	yes	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{155}(23,\cdot)\)	155.r	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{155}(24,\cdot)\)	155.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{155}(26,\cdot)\)	155.k	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{155}(27,\cdot)\)	155.r	20	yes	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{155}(28,\cdot)\)	155.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{155}(29,\cdot)\)	155.m	10	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{155}(32,\cdot)\)	155.g	4	no	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{155}(33,\cdot)\)	155.s	20	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{155}(34,\cdot)\)	155.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{155}(36,\cdot)\)	155.e	3	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{155}(37,\cdot)\)	155.p	12	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{155}(38,\cdot)\)	155.w	60	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{155}(39,\cdot)\)	155.n	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{155}(41,\cdot)\)	155.q	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)

Introduction

L-functions

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Character group

First 32 of 120 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.