LMFDB - Group of Dirichlet characters of modulus 261

Show commands: PariGP / SageMath

sage: H = DirichletGroup(261)

pari: g = idealstar(,261,2)

Character group

sage: G.order() pari: g.no
Order	=	168
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{84}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{261}(146,\cdot)$, $\chi_{261}(118,\cdot)$

First 32 of 168 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{261}(1,\cdot)$	261.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{261}(2,\cdot)$	261.x	84	yes	$1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{261}(4,\cdot)$	261.u	42	yes	$1$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{261}(5,\cdot)$	261.v	42	yes	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{261}(7,\cdot)$	261.q	21	yes	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{261}(8,\cdot)$	261.r	28	no	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{261}(10,\cdot)$	261.s	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{261}(11,\cdot)$	261.x	84	yes	$1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{261}(13,\cdot)$	261.u	42	yes	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{261}(14,\cdot)$	261.x	84	yes	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{261}(16,\cdot)$	261.q	21	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{261}(17,\cdot)$	261.g	4	no	$1$	$1$	$i$	$-1$	$1$	$1$	$-i$	$i$	$i$	$-1$	$i$	$1$
$\chi_{261}(19,\cdot)$	261.s	28	no	$-1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{261}(20,\cdot)$	261.t	42	yes	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{261}(22,\cdot)$	261.u	42	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{261}(23,\cdot)$	261.t	42	yes	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{261}(25,\cdot)$	261.q	21	yes	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{261}(26,\cdot)$	261.r	28	no	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{261}(28,\cdot)$	261.c	2	no	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$1$
$\chi_{261}(31,\cdot)$	261.w	84	yes	$-1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{261}(32,\cdot)$	261.x	84	yes	$1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{261}(34,\cdot)$	261.u	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{261}(35,\cdot)$	261.n	14	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{261}(37,\cdot)$	261.s	28	no	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{261}(38,\cdot)$	261.v	42	yes	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{261}(40,\cdot)$	261.w	84	yes	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{261}(41,\cdot)$	261.l	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{261}(43,\cdot)$	261.w	84	yes	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{261}(44,\cdot)$	261.r	28	no	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{261}(46,\cdot)$	261.f	4	no	$-1$	$1$	$-i$	$-1$	$-1$	$1$	$i$	$i$	$-i$	$-1$	$-i$	$1$
$\chi_{261}(47,\cdot)$	261.x	84	yes	$1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{261}(49,\cdot)$	261.q	21	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$

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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	$261$
Structure	\(C_{2}\times C_{84}\)
Order	$168$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{261}(1,\cdot)\)	261.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{261}(2,\cdot)\)	261.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{261}(4,\cdot)\)	261.u	42	yes	\(1\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{261}(5,\cdot)\)	261.v	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{261}(7,\cdot)\)	261.q	21	yes	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{261}(8,\cdot)\)	261.r	28	no	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{261}(10,\cdot)\)	261.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{261}(11,\cdot)\)	261.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{261}(13,\cdot)\)	261.u	42	yes	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{261}(14,\cdot)\)	261.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{261}(16,\cdot)\)	261.q	21	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{261}(17,\cdot)\)	261.g	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)
\(\chi_{261}(19,\cdot)\)	261.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{261}(20,\cdot)\)	261.t	42	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{261}(22,\cdot)\)	261.u	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{261}(23,\cdot)\)	261.t	42	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{261}(25,\cdot)\)	261.q	21	yes	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{261}(26,\cdot)\)	261.r	28	no	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{261}(28,\cdot)\)	261.c	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{261}(31,\cdot)\)	261.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{261}(32,\cdot)\)	261.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{261}(34,\cdot)\)	261.u	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{261}(35,\cdot)\)	261.n	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{261}(37,\cdot)\)	261.s	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{261}(38,\cdot)\)	261.v	42	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{261}(40,\cdot)\)	261.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{261}(41,\cdot)\)	261.l	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{261}(43,\cdot)\)	261.w	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{261}(44,\cdot)\)	261.r	28	no	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{261}(46,\cdot)\)	261.f	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{261}(47,\cdot)\)	261.x	84	yes	\(1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{261}(49,\cdot)\)	261.q	21	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)

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L-functions

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First 32 of 168 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.