LMFDB - Group of Dirichlet characters of modulus 1368

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1368)

pari: g = idealstar(,1368,2)

Character group

sage: G.order() pari: g.no
Order	=	432
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{18}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1368}(343,\cdot)$, $\chi_{1368}(685,\cdot)$, $\chi_{1368}(1217,\cdot)$, $\chi_{1368}(1009,\cdot)$

First 32 of 432 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{1368}(1,\cdot)$	1368.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1368}(5,\cdot)$	1368.ea	18	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{5}{9}\right)$
$\chi_{1368}(7,\cdot)$	1368.bs	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1368}(11,\cdot)$	1368.db	6	yes	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1368}(13,\cdot)$	1368.ex	18	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1368}(17,\cdot)$	1368.dv	18	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1368}(23,\cdot)$	1368.di	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1368}(25,\cdot)$	1368.dd	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{1}{9}\right)$
$\chi_{1368}(29,\cdot)$	1368.dz	18	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{7}{9}\right)$
$\chi_{1368}(31,\cdot)$	1368.da	6	no	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1368}(35,\cdot)$	1368.el	18	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1368}(37,\cdot)$	1368.i	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$
$\chi_{1368}(41,\cdot)$	1368.dn	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{7}{18}\right)$
$\chi_{1368}(43,\cdot)$	1368.dh	18	yes	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1368}(47,\cdot)$	1368.eo	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{7}{9}\right)$
$\chi_{1368}(49,\cdot)$	1368.r	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1368}(53,\cdot)$	1368.dt	18	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1368}(55,\cdot)$	1368.em	18	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{1368}(59,\cdot)$	1368.ee	18	yes	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{13}{18}\right)$
$\chi_{1368}(61,\cdot)$	1368.dp	18	yes	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$1$	$e\left(\frac{17}{18}\right)$
$\chi_{1368}(65,\cdot)$	1368.x	6	no	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1368}(67,\cdot)$	1368.dg	18	yes	$1$	$1$	$e\left(\frac{5}{18}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1368}(71,\cdot)$	1368.ef	18	no	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1368}(73,\cdot)$	1368.dc	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1368}(77,\cdot)$	1368.bj	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{1368}(79,\cdot)$	1368.dj	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1368}(83,\cdot)$	1368.bn	6	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1368}(85,\cdot)$	1368.eu	18	yes	$1$	$1$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{1368}(89,\cdot)$	1368.dw	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1368}(91,\cdot)$	1368.eg	18	no	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1368}(97,\cdot)$	1368.es	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1368}(101,\cdot)$	1368.ea	18	yes	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{1}{9}\right)$

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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	$1368$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{18}\)
Order	$432$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{1368}(1,\cdot)\)	1368.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1368}(5,\cdot)\)	1368.ea	18	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1368}(7,\cdot)\)	1368.bs	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1368}(11,\cdot)\)	1368.db	6	yes	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1368}(13,\cdot)\)	1368.ex	18	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1368}(17,\cdot)\)	1368.dv	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1368}(23,\cdot)\)	1368.di	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1368}(25,\cdot)\)	1368.dd	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1368}(29,\cdot)\)	1368.dz	18	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(-1\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1368}(31,\cdot)\)	1368.da	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1368}(35,\cdot)\)	1368.el	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1368}(37,\cdot)\)	1368.i	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{1368}(41,\cdot)\)	1368.dn	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1368}(43,\cdot)\)	1368.dh	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1368}(47,\cdot)\)	1368.eo	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(-1\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1368}(49,\cdot)\)	1368.r	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1368}(53,\cdot)\)	1368.dt	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1368}(55,\cdot)\)	1368.em	18	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1368}(59,\cdot)\)	1368.ee	18	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{1368}(61,\cdot)\)	1368.dp	18	yes	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1368}(65,\cdot)\)	1368.x	6	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1368}(67,\cdot)\)	1368.dg	18	yes	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1368}(71,\cdot)\)	1368.ef	18	no	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1368}(73,\cdot)\)	1368.dc	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1368}(77,\cdot)\)	1368.bj	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{1368}(79,\cdot)\)	1368.dj	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1368}(83,\cdot)\)	1368.bn	6	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1368}(85,\cdot)\)	1368.eu	18	yes	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{1368}(89,\cdot)\)	1368.dw	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1368}(91,\cdot)\)	1368.eg	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1368}(97,\cdot)\)	1368.es	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1368}(101,\cdot)\)	1368.ea	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)

Introduction

L-functions

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Character group

First 32 of 432 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.