LMFDB - Group of Dirichlet characters of modulus 1380

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1380)

pari: g = idealstar(,1380,2)

Character group

sage: G.order() pari: g.no
Order	=	352
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{44}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1380}(691,\cdot)$, $\chi_{1380}(461,\cdot)$, $\chi_{1380}(277,\cdot)$, $\chi_{1380}(1201,\cdot)$

First 32 of 352 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$29$	$31$	$37$	$41$	$43$
$\chi_{1380}(1,\cdot)$	1380.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1380}(7,\cdot)$	1380.br	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{1380}(11,\cdot)$	1380.bc	22	no	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{1380}(13,\cdot)$	1380.bq	44	no	$-1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{1380}(17,\cdot)$	1380.bo	44	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{44}\right)$
$\chi_{1380}(19,\cdot)$	1380.bi	22	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1380}(29,\cdot)$	1380.bm	22	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{1380}(31,\cdot)$	1380.bk	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{1380}(37,\cdot)$	1380.bs	44	no	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{1380}(41,\cdot)$	1380.bd	22	no	$-1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1380}(43,\cdot)$	1380.br	44	no	$-1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{1380}(47,\cdot)$	1380.w	4	no	$-1$	$1$	$-i$	$1$	$-i$	$-i$	$1$	$1$	$-1$	$i$	$-1$	$i$
$\chi_{1380}(49,\cdot)$	1380.bj	22	no	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{1380}(53,\cdot)$	1380.bo	44	no	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{1380}(59,\cdot)$	1380.ba	22	yes	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{1380}(61,\cdot)$	1380.bl	22	no	$-1$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{1380}(67,\cdot)$	1380.br	44	no	$-1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{1380}(71,\cdot)$	1380.bh	22	no	$1$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{1380}(73,\cdot)$	1380.bq	44	no	$-1$	$1$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{1380}(77,\cdot)$	1380.bu	44	no	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{1380}(79,\cdot)$	1380.bi	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{1380}(83,\cdot)$	1380.bv	44	yes	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{1380}(89,\cdot)$	1380.bb	22	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{1380}(91,\cdot)$	1380.p	2	no	$1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$
$\chi_{1380}(97,\cdot)$	1380.bs	44	no	$1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{1380}(101,\cdot)$	1380.bd	22	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{1380}(103,\cdot)$	1380.br	44	no	$-1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{1380}(107,\cdot)$	1380.bv	44	yes	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{1380}(109,\cdot)$	1380.be	22	no	$-1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{1380}(113,\cdot)$	1380.bo	44	no	$-1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{1380}(119,\cdot)$	1380.ba	22	yes	$1$	$1$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{1380}(121,\cdot)$	1380.y	11	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$

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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	$1380$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{44}\)
Order	$352$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{1380}(1,\cdot)\)	1380.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1380}(7,\cdot)\)	1380.br	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{1380}(11,\cdot)\)	1380.bc	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{1380}(13,\cdot)\)	1380.bq	44	no	\(-1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{1380}(17,\cdot)\)	1380.bo	44	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)
\(\chi_{1380}(19,\cdot)\)	1380.bi	22	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1380}(29,\cdot)\)	1380.bm	22	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{1380}(31,\cdot)\)	1380.bk	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{1380}(37,\cdot)\)	1380.bs	44	no	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{1380}(41,\cdot)\)	1380.bd	22	no	\(-1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1380}(43,\cdot)\)	1380.br	44	no	\(-1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{1380}(47,\cdot)\)	1380.w	4	no	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(i\)
\(\chi_{1380}(49,\cdot)\)	1380.bj	22	no	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{1380}(53,\cdot)\)	1380.bo	44	no	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{1380}(59,\cdot)\)	1380.ba	22	yes	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{1380}(61,\cdot)\)	1380.bl	22	no	\(-1\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{1380}(67,\cdot)\)	1380.br	44	no	\(-1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{1380}(71,\cdot)\)	1380.bh	22	no	\(1\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{1380}(73,\cdot)\)	1380.bq	44	no	\(-1\)	\(1\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{1380}(77,\cdot)\)	1380.bu	44	no	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{1380}(79,\cdot)\)	1380.bi	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{1380}(83,\cdot)\)	1380.bv	44	yes	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{1380}(89,\cdot)\)	1380.bb	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{1380}(91,\cdot)\)	1380.p	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{1380}(97,\cdot)\)	1380.bs	44	no	\(1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{1380}(101,\cdot)\)	1380.bd	22	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{1380}(103,\cdot)\)	1380.br	44	no	\(-1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{1380}(107,\cdot)\)	1380.bv	44	yes	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{1380}(109,\cdot)\)	1380.be	22	no	\(-1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{1380}(113,\cdot)\)	1380.bo	44	no	\(-1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{1380}(119,\cdot)\)	1380.ba	22	yes	\(1\)	\(1\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{1380}(121,\cdot)\)	1380.y	11	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)

Introduction

L-functions

Modular forms

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Groups

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Properties

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Character group

First 32 of 352 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.