LMFDB - Group of Dirichlet characters of modulus 1407

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1407)

pari: g = idealstar(,1407,2)

Character group

sage: G.order() pari: g.no
Order	=	792
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{66}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1407}(470,\cdot)$, $\chi_{1407}(1207,\cdot)$, $\chi_{1407}(337,\cdot)$

First 32 of 792 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{1407}(1,\cdot)$	1407.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1407}(2,\cdot)$	1407.cc	66	yes	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{1407}(4,\cdot)$	1407.bw	33	no	$1$	$1$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{1407}(5,\cdot)$	1407.cq	66	yes	$-1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{1407}(8,\cdot)$	1407.bp	22	no	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{1407}(10,\cdot)$	1407.cs	66	no	$-1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{1407}(11,\cdot)$	1407.cc	66	yes	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{1407}(13,\cdot)$	1407.ce	66	no	$1$	$1$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{1407}(16,\cdot)$	1407.bw	33	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{1407}(17,\cdot)$	1407.cl	66	yes	$1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{1407}(19,\cdot)$	1407.ca	66	no	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{1407}(20,\cdot)$	1407.cx	66	yes	$-1$	$1$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{1407}(22,\cdot)$	1407.bo	11	no	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{1407}(23,\cdot)$	1407.cz	66	yes	$-1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{1407}(25,\cdot)$	1407.bz	33	no	$1$	$1$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{1407}(26,\cdot)$	1407.cl	66	yes	$1$	$1$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{1407}(29,\cdot)$	1407.z	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1407}(31,\cdot)$	1407.db	66	no	$1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{1407}(32,\cdot)$	1407.cc	66	yes	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{1407}(34,\cdot)$	1407.ce	66	no	$1$	$1$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{23}{66}\right)$
$\chi_{1407}(37,\cdot)$	1407.l	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{1407}(38,\cdot)$	1407.bm	6	yes	$-1$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{1407}(40,\cdot)$	1407.cr	66	no	$-1$	$1$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{1407}(41,\cdot)$	1407.cx	66	yes	$-1$	$1$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{35}{66}\right)$
$\chi_{1407}(43,\cdot)$	1407.bv	22	no	$-1$	$1$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{1407}(44,\cdot)$	1407.cc	66	yes	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{1407}(46,\cdot)$	1407.cy	66	no	$-1$	$1$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{1407}(47,\cdot)$	1407.cl	66	yes	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{1407}(50,\cdot)$	1407.cp	66	no	$1$	$1$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{1407}(52,\cdot)$	1407.cj	66	no	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{1407}(53,\cdot)$	1407.cv	66	yes	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{1407}(55,\cdot)$	1407.cw	66	no	$-1$	$1$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{47}{66}\right)$

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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	$1407$
Structure	\(C_{2}\times C_{6}\times C_{66}\)
Order	$792$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{1407}(1,\cdot)\)	1407.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1407}(2,\cdot)\)	1407.cc	66	yes	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{1407}(4,\cdot)\)	1407.bw	33	no	\(1\)	\(1\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{1407}(5,\cdot)\)	1407.cq	66	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{1407}(8,\cdot)\)	1407.bp	22	no	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{1407}(10,\cdot)\)	1407.cs	66	no	\(-1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{1407}(11,\cdot)\)	1407.cc	66	yes	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{1407}(13,\cdot)\)	1407.ce	66	no	\(1\)	\(1\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{1407}(16,\cdot)\)	1407.bw	33	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{1407}(17,\cdot)\)	1407.cl	66	yes	\(1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{1407}(19,\cdot)\)	1407.ca	66	no	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{1407}(20,\cdot)\)	1407.cx	66	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{1407}(22,\cdot)\)	1407.bo	11	no	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{1407}(23,\cdot)\)	1407.cz	66	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{1407}(25,\cdot)\)	1407.bz	33	no	\(1\)	\(1\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{1407}(26,\cdot)\)	1407.cl	66	yes	\(1\)	\(1\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{1407}(29,\cdot)\)	1407.z	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1407}(31,\cdot)\)	1407.db	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{1407}(32,\cdot)\)	1407.cc	66	yes	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{1407}(34,\cdot)\)	1407.ce	66	no	\(1\)	\(1\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)
\(\chi_{1407}(37,\cdot)\)	1407.l	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{1407}(38,\cdot)\)	1407.bm	6	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{1407}(40,\cdot)\)	1407.cr	66	no	\(-1\)	\(1\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{1407}(41,\cdot)\)	1407.cx	66	yes	\(-1\)	\(1\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)
\(\chi_{1407}(43,\cdot)\)	1407.bv	22	no	\(-1\)	\(1\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{1407}(44,\cdot)\)	1407.cc	66	yes	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{1407}(46,\cdot)\)	1407.cy	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{1407}(47,\cdot)\)	1407.cl	66	yes	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{1407}(50,\cdot)\)	1407.cp	66	no	\(1\)	\(1\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{1407}(52,\cdot)\)	1407.cj	66	no	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{1407}(53,\cdot)\)	1407.cv	66	yes	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{1407}(55,\cdot)\)	1407.cw	66	no	\(-1\)	\(1\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.