LMFDB - Group of Dirichlet characters of modulus 1335

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1335)

pari: g = idealstar(,1335,2)

Character group

sage: G.order() pari: g.no
Order	=	704
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{88}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1335}(446,\cdot)$, $\chi_{1335}(802,\cdot)$, $\chi_{1335}(181,\cdot)$

First 32 of 704 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1335}(1,\cdot)$	1335.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1335}(2,\cdot)$	1335.bq	44	yes	$1$	$1$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{1335}(4,\cdot)$	1335.bi	22	no	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1335}(7,\cdot)$	1335.cb	88	no	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{63}{88}\right)$
$\chi_{1335}(8,\cdot)$	1335.bq	44	yes	$1$	$1$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{1335}(11,\cdot)$	1335.bj	22	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{1335}(13,\cdot)$	1335.cb	88	no	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{57}{88}\right)$
$\chi_{1335}(14,\cdot)$	1335.bw	88	yes	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{51}{88}\right)$
$\chi_{1335}(16,\cdot)$	1335.bc	11	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{1335}(17,\cdot)$	1335.bt	44	yes	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{1335}(19,\cdot)$	1335.cd	88	no	$-1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{81}{88}\right)$
$\chi_{1335}(22,\cdot)$	1335.bo	44	no	$-1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{1335}(23,\cdot)$	1335.bz	88	yes	$-1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{15}{88}\right)$
$\chi_{1335}(26,\cdot)$	1335.cc	88	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{45}{88}\right)$
$\chi_{1335}(28,\cdot)$	1335.ca	88	no	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{39}{88}\right)$
$\chi_{1335}(29,\cdot)$	1335.bw	88	yes	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{41}{88}\right)$
$\chi_{1335}(31,\cdot)$	1335.bx	88	no	$-1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{1335}(32,\cdot)$	1335.bq	44	yes	$1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{1335}(34,\cdot)$	1335.j	4	no	$1$	$1$	$-1$	$1$	$-i$	$-1$	$1$	$i$	$i$	$1$	$1$	$-i$
$\chi_{1335}(37,\cdot)$	1335.x	8	no	$1$	$1$	$i$	$-1$	$e\left(\frac{3}{8}\right)$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$1$	$e\left(\frac{7}{8}\right)$
$\chi_{1335}(38,\cdot)$	1335.by	88	yes	$-1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{69}{88}\right)$
$\chi_{1335}(41,\cdot)$	1335.cc	88	no	$1$	$1$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{31}{88}\right)$
$\chi_{1335}(43,\cdot)$	1335.ca	88	no	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{1335}(44,\cdot)$	1335.bd	22	yes	$-1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{1335}(46,\cdot)$	1335.bx	88	no	$-1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{3}{88}\right)$
$\chi_{1335}(47,\cdot)$	1335.bt	44	yes	$1$	$1$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{1335}(49,\cdot)$	1335.bu	44	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{1335}(52,\cdot)$	1335.x	8	no	$1$	$1$	$i$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$1$	$e\left(\frac{3}{8}\right)$
$\chi_{1335}(53,\cdot)$	1335.bn	44	yes	$1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{1335}(56,\cdot)$	1335.cc	88	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{27}{88}\right)$
$\chi_{1335}(58,\cdot)$	1335.cb	88	no	$1$	$1$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{29}{88}\right)$
$\chi_{1335}(59,\cdot)$	1335.bw	88	yes	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{65}{88}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{88}\right)$

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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	$1335$
Structure	\(C_{2}\times C_{4}\times C_{88}\)
Order	$704$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1335}(1,\cdot)\)	1335.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1335}(2,\cdot)\)	1335.bq	44	yes	\(1\)	\(1\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{1335}(4,\cdot)\)	1335.bi	22	no	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1335}(7,\cdot)\)	1335.cb	88	no	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{63}{88}\right)\)
\(\chi_{1335}(8,\cdot)\)	1335.bq	44	yes	\(1\)	\(1\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{1335}(11,\cdot)\)	1335.bj	22	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{1335}(13,\cdot)\)	1335.cb	88	no	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)
\(\chi_{1335}(14,\cdot)\)	1335.bw	88	yes	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{51}{88}\right)\)
\(\chi_{1335}(16,\cdot)\)	1335.bc	11	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{1335}(17,\cdot)\)	1335.bt	44	yes	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{1335}(19,\cdot)\)	1335.cd	88	no	\(-1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)
\(\chi_{1335}(22,\cdot)\)	1335.bo	44	no	\(-1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{1335}(23,\cdot)\)	1335.bz	88	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)
\(\chi_{1335}(26,\cdot)\)	1335.cc	88	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)
\(\chi_{1335}(28,\cdot)\)	1335.ca	88	no	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{39}{88}\right)\)
\(\chi_{1335}(29,\cdot)\)	1335.bw	88	yes	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)
\(\chi_{1335}(31,\cdot)\)	1335.bx	88	no	\(-1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{1335}(32,\cdot)\)	1335.bq	44	yes	\(1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{1335}(34,\cdot)\)	1335.j	4	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(1\)	\(-i\)
\(\chi_{1335}(37,\cdot)\)	1335.x	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1335}(38,\cdot)\)	1335.by	88	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{69}{88}\right)\)
\(\chi_{1335}(41,\cdot)\)	1335.cc	88	no	\(1\)	\(1\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)
\(\chi_{1335}(43,\cdot)\)	1335.ca	88	no	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{1335}(44,\cdot)\)	1335.bd	22	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{1335}(46,\cdot)\)	1335.bx	88	no	\(-1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{3}{88}\right)\)
\(\chi_{1335}(47,\cdot)\)	1335.bt	44	yes	\(1\)	\(1\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{1335}(49,\cdot)\)	1335.bu	44	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{1335}(52,\cdot)\)	1335.x	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1335}(53,\cdot)\)	1335.bn	44	yes	\(1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{1335}(56,\cdot)\)	1335.cc	88	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{27}{88}\right)\)
\(\chi_{1335}(58,\cdot)\)	1335.cb	88	no	\(1\)	\(1\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{29}{88}\right)\)
\(\chi_{1335}(59,\cdot)\)	1335.bw	88	yes	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{65}{88}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)

Introduction

L-functions

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Character group

First 32 of 704 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.