LMFDB - Group of Dirichlet characters of modulus 1638

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1638)

pari: g = idealstar(,1638,2)

Character group

sage: G.order() pari: g.no
Order	=	432
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{6}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1638}(911,\cdot)$, $\chi_{1638}(703,\cdot)$, $\chi_{1638}(379,\cdot)$

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	$-1$	$1$	$5$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{1638}(1,\cdot)$	1638.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1638}(5,\cdot)$	1638.ft	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1638}(11,\cdot)$	1638.fk	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1638}(17,\cdot)$	1638.dg	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{1638}(19,\cdot)$	1638.fg	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1638}(23,\cdot)$	1638.cn	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$
$\chi_{1638}(25,\cdot)$	1638.dl	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1638}(29,\cdot)$	1638.ct	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1638}(31,\cdot)$	1638.eu	12	no	$1$	$1$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1638}(37,\cdot)$	1638.em	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$
$\chi_{1638}(41,\cdot)$	1638.gd	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{1638}(43,\cdot)$	1638.dn	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{1638}(47,\cdot)$	1638.gb	12	no	$-1$	$1$	$i$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1638}(53,\cdot)$	1638.dp	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{1638}(55,\cdot)$	1638.bf	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1638}(59,\cdot)$	1638.en	12	no	$-1$	$1$	$i$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$
$\chi_{1638}(61,\cdot)$	1638.be	6	no	$-1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{1638}(67,\cdot)$	1638.fv	12	no	$-1$	$1$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-i$
$\chi_{1638}(71,\cdot)$	1638.ey	12	no	$1$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1638}(73,\cdot)$	1638.fh	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{1638}(79,\cdot)$	1638.u	3	no	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1638}(83,\cdot)$	1638.ep	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$
$\chi_{1638}(85,\cdot)$	1638.ga	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1638}(89,\cdot)$	1638.et	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{7}{12}\right)$
$\chi_{1638}(95,\cdot)$	1638.ec	6	no	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{1638}(97,\cdot)$	1638.ev	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{1638}(101,\cdot)$	1638.db	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1638}(103,\cdot)$	1638.ch	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1638}(107,\cdot)$	1638.di	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{1638}(109,\cdot)$	1638.fz	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{1638}(113,\cdot)$	1638.ct	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1638}(115,\cdot)$	1638.ew	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$

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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	$1638$
Structure	\(C_{6}\times C_{6}\times C_{12}\)
Order	$432$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{1638}(1,\cdot)\)	1638.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1638}(5,\cdot)\)	1638.ft	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1638}(11,\cdot)\)	1638.fk	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1638}(17,\cdot)\)	1638.dg	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1638}(19,\cdot)\)	1638.fg	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1638}(23,\cdot)\)	1638.cn	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{1638}(25,\cdot)\)	1638.dl	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1638}(29,\cdot)\)	1638.ct	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1638}(31,\cdot)\)	1638.eu	12	no	\(1\)	\(1\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1638}(37,\cdot)\)	1638.em	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1638}(41,\cdot)\)	1638.gd	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{1638}(43,\cdot)\)	1638.dn	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{1638}(47,\cdot)\)	1638.gb	12	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1638}(53,\cdot)\)	1638.dp	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{1638}(55,\cdot)\)	1638.bf	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1638}(59,\cdot)\)	1638.en	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1638}(61,\cdot)\)	1638.be	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{1638}(67,\cdot)\)	1638.fv	12	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)
\(\chi_{1638}(71,\cdot)\)	1638.ey	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1638}(73,\cdot)\)	1638.fh	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)
\(\chi_{1638}(79,\cdot)\)	1638.u	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1638}(83,\cdot)\)	1638.ep	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1638}(85,\cdot)\)	1638.ga	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1638}(89,\cdot)\)	1638.et	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1638}(95,\cdot)\)	1638.ec	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1638}(97,\cdot)\)	1638.ev	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{1638}(101,\cdot)\)	1638.db	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1638}(103,\cdot)\)	1638.ch	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1638}(107,\cdot)\)	1638.di	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1638}(109,\cdot)\)	1638.fz	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{1638}(113,\cdot)\)	1638.ct	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1638}(115,\cdot)\)	1638.ew	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)

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.