LMFDB - Group of Dirichlet characters of modulus 138

Show commands: PariGP / SageMath

sage: H = DirichletGroup(138)

pari: g = idealstar(,138,2)

Character group

sage: G.order() pari: g.no
Order	=	44
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{22}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{138}(47,\cdot)$, $\chi_{138}(97,\cdot)$

First 32 of 44 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$25$	$29$	$31$	$35$
$\chi_{138}(1,\cdot)$	138.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{138}(5,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{138}(7,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{138}(11,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{138}(13,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{138}(17,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{138}(19,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{138}(25,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{138}(29,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{138}(31,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{138}(35,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{138}(37,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{138}(41,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{138}(43,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{138}(47,\cdot)$	138.c	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$
$\chi_{138}(49,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{138}(53,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{138}(55,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{138}(59,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{138}(61,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{138}(65,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{138}(67,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{138}(71,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{138}(73,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{138}(77,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{138}(79,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{138}(83,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{138}(85,\cdot)$	138.e	11	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{138}(89,\cdot)$	138.f	22	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{138}(91,\cdot)$	138.b	2	no	$-1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{138}(95,\cdot)$	138.g	22	no	$-1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{138}(97,\cdot)$	138.h	22	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{11}\right)$

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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	$138$
Structure	\(C_{2}\times C_{22}\)
Order	$44$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{138}(1,\cdot)\)	138.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{138}(5,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{138}(7,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{138}(11,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{138}(13,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{138}(17,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{138}(19,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{138}(25,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{138}(29,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{138}(31,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{138}(35,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{138}(37,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{138}(41,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{138}(43,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{138}(47,\cdot)\)	138.c	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)
\(\chi_{138}(49,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{138}(53,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{138}(55,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{138}(59,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{138}(61,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{138}(65,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{138}(67,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{138}(71,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{138}(73,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{138}(77,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{138}(79,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{138}(83,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{138}(85,\cdot)\)	138.e	11	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{138}(89,\cdot)\)	138.f	22	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{138}(91,\cdot)\)	138.b	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{138}(95,\cdot)\)	138.g	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{138}(97,\cdot)\)	138.h	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)

Introduction

L-functions

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Properties

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Character group

First 32 of 44 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.