LMFDB - Group of Dirichlet characters of modulus 92

Show commands: PariGP / SageMath

sage: H = DirichletGroup(92)

pari: g = idealstar(,92,2)

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	=	$\chi_{92}(47,\cdot)$, $\chi_{92}(5,\cdot)$

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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{92}(1,\cdot)$	92.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{92}(3,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{92}(5,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{92}(7,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{92}(9,\cdot)$	92.e	11	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{92}(11,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{92}(13,\cdot)$	92.e	11	no	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{92}(15,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{92}(17,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{92}(19,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{92}(21,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{92}(25,\cdot)$	92.e	11	no	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{92}(27,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{92}(29,\cdot)$	92.e	11	no	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{92}(31,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{92}(33,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{17}{22}\right)$
$\chi_{92}(35,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{92}(37,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{92}(39,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{92}(41,\cdot)$	92.e	11	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{92}(43,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{92}(45,\cdot)$	92.d	2	no	$-1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$
$\chi_{92}(47,\cdot)$	92.c	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{92}(49,\cdot)$	92.e	11	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{92}(51,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{92}(53,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{92}(55,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{92}(57,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{92}(59,\cdot)$	92.g	22	yes	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{92}(61,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{92}(63,\cdot)$	92.h	22	yes	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{92}(65,\cdot)$	92.f	22	no	$-1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{22}\right)$

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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	$92$
Structure	\(C_{2}\times C_{22}\)
Order	$44$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{92}(1,\cdot)\)	92.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{92}(3,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{92}(5,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{92}(7,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{92}(9,\cdot)\)	92.e	11	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{92}(11,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{92}(13,\cdot)\)	92.e	11	no	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{92}(15,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{92}(17,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{92}(19,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{92}(21,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{92}(25,\cdot)\)	92.e	11	no	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{92}(27,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{92}(29,\cdot)\)	92.e	11	no	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{92}(31,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{92}(33,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{92}(35,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{92}(37,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{92}(39,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{92}(41,\cdot)\)	92.e	11	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{92}(43,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{92}(45,\cdot)\)	92.d	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{92}(47,\cdot)\)	92.c	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{92}(49,\cdot)\)	92.e	11	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{92}(51,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{92}(53,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{92}(55,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{92}(57,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{92}(59,\cdot)\)	92.g	22	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{92}(61,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{92}(63,\cdot)\)	92.h	22	yes	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{92}(65,\cdot)\)	92.f	22	no	\(-1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)

Introduction

L-functions

Modular forms

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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.