LMFDB - Group of Dirichlet characters of modulus 381

sage:H = DirichletGroup(381)

pari:g = idealstar(,381,2)

Character group

sage:G.order() pari:g.no
Order	=	252
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{126}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{381}(128,\cdot)$, $\chi_{381}(130,\cdot)$

First 32 of 252 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{381}(1,\cdot)$	381.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{381}(2,\cdot)$	381.m	14	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{381}(4,\cdot)$	381.i	7	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{381}(5,\cdot)$	381.s	42	yes	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{381}(7,\cdot)$	381.v	126	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{381}(8,\cdot)$	381.m	14	yes	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{381}(10,\cdot)$	381.r	42	no	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{381}(11,\cdot)$	381.w	126	yes	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{381}(13,\cdot)$	381.u	63	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{381}(14,\cdot)$	381.x	126	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{381}(16,\cdot)$	381.i	7	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{381}(17,\cdot)$	381.w	126	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{381}(19,\cdot)$	381.e	3	no	$1$	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{381}(20,\cdot)$	381.g	6	yes	$1$	$1$	$-1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{381}(22,\cdot)$	381.j	9	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$
$\chi_{381}(23,\cdot)$	381.x	126	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{381}(25,\cdot)$	381.q	21	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{381}(26,\cdot)$	381.w	126	yes	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{381}(28,\cdot)$	381.p	18	no	$-1$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$1$
$\chi_{381}(29,\cdot)$	381.x	126	yes	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{381}(31,\cdot)$	381.u	63	no	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{381}(32,\cdot)$	381.m	14	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{381}(34,\cdot)$	381.u	63	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{381}(35,\cdot)$	381.w	126	yes	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{381}(37,\cdot)$	381.j	9	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$1$
$\chi_{381}(38,\cdot)$	381.t	42	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{381}(40,\cdot)$	381.r	42	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{381}(41,\cdot)$	381.w	126	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{381}(43,\cdot)$	381.v	126	no	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{381}(44,\cdot)$	381.w	126	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{381}(46,\cdot)$	381.v	126	no	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{381}(47,\cdot)$	381.t	42	yes	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{7}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$381$
Structure	\(C_{2}\times C_{126}\)
Order	$252$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{381}(1,\cdot)\)	381.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{381}(2,\cdot)\)	381.m	14	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{381}(4,\cdot)\)	381.i	7	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{381}(5,\cdot)\)	381.s	42	yes	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{381}(7,\cdot)\)	381.v	126	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{381}(8,\cdot)\)	381.m	14	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{381}(10,\cdot)\)	381.r	42	no	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{381}(11,\cdot)\)	381.w	126	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{381}(13,\cdot)\)	381.u	63	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{381}(14,\cdot)\)	381.x	126	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{381}(16,\cdot)\)	381.i	7	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{381}(17,\cdot)\)	381.w	126	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{381}(19,\cdot)\)	381.e	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{381}(20,\cdot)\)	381.g	6	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{381}(22,\cdot)\)	381.j	9	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)
\(\chi_{381}(23,\cdot)\)	381.x	126	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{381}(25,\cdot)\)	381.q	21	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{381}(26,\cdot)\)	381.w	126	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{381}(28,\cdot)\)	381.p	18	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(1\)
\(\chi_{381}(29,\cdot)\)	381.x	126	yes	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{381}(31,\cdot)\)	381.u	63	no	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{381}(32,\cdot)\)	381.m	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{381}(34,\cdot)\)	381.u	63	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{381}(35,\cdot)\)	381.w	126	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{381}(37,\cdot)\)	381.j	9	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)
\(\chi_{381}(38,\cdot)\)	381.t	42	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{381}(40,\cdot)\)	381.r	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{381}(41,\cdot)\)	381.w	126	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{381}(43,\cdot)\)	381.v	126	no	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{381}(44,\cdot)\)	381.w	126	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{381}(46,\cdot)\)	381.v	126	no	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{381}(47,\cdot)\)	381.t	42	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)

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L-functions

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First 32 of 252 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.