LMFDB - Group of Dirichlet characters of modulus 1170

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1170)

pari: g = idealstar(,1170,2)

Character group

sage: G.order() pari: g.no
Order	=	288
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{12}\times C_{12}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1170}(911,\cdot)$, $\chi_{1170}(937,\cdot)$, $\chi_{1170}(1081,\cdot)$

First 32 of 288 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	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{1170}(1,\cdot)$	1170.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1170}(7,\cdot)$	1170.dv	12	no	$1$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$i$
$\chi_{1170}(11,\cdot)$	1170.cs	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1170}(17,\cdot)$	1170.cl	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1170}(19,\cdot)$	1170.ct	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1170}(23,\cdot)$	1170.cm	12	no	$1$	$1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$i$
$\chi_{1170}(29,\cdot)$	1170.bl	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1170}(31,\cdot)$	1170.cq	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1170}(37,\cdot)$	1170.cf	12	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1170}(41,\cdot)$	1170.cx	12	no	$1$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$-1$
$\chi_{1170}(43,\cdot)$	1170.di	12	no	$-1$	$1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$i$
$\chi_{1170}(47,\cdot)$	1170.ce	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1170}(49,\cdot)$	1170.bz	6	no	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$
$\chi_{1170}(53,\cdot)$	1170.o	4	no	$1$	$1$	$-i$	$-1$	$i$	$-1$	$-i$	$1$	$1$	$-i$	$-1$	$i$
$\chi_{1170}(59,\cdot)$	1170.da	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1170}(61,\cdot)$	1170.l	3	no	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$
$\chi_{1170}(67,\cdot)$	1170.cb	12	no	$1$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$i$
$\chi_{1170}(71,\cdot)$	1170.cu	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1170}(73,\cdot)$	1170.m	4	no	$1$	$1$	$-1$	$-i$	$i$	$-i$	$-i$	$-1$	$i$	$-1$	$i$	$-i$
$\chi_{1170}(77,\cdot)$	1170.cp	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1170}(79,\cdot)$	1170.bo	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1170}(83,\cdot)$	1170.ce	12	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1170}(89,\cdot)$	1170.dc	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1170}(97,\cdot)$	1170.cb	12	no	$1$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$i$
$\chi_{1170}(101,\cdot)$	1170.bw	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1170}(103,\cdot)$	1170.dl	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{1170}(107,\cdot)$	1170.dk	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1170}(109,\cdot)$	1170.t	4	no	$-1$	$1$	$-i$	$i$	$1$	$-i$	$1$	$1$	$-i$	$-i$	$-i$	$1$
$\chi_{1170}(113,\cdot)$	1170.cj	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1170}(119,\cdot)$	1170.da	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{1170}(121,\cdot)$	1170.bm	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1170}(127,\cdot)$	1170.dh	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$

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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	$1170$
Structure	\(C_{2}\times C_{12}\times C_{12}\)
Order	$288$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{1170}(1,\cdot)\)	1170.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1170}(7,\cdot)\)	1170.dv	12	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(i\)
\(\chi_{1170}(11,\cdot)\)	1170.cs	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(17,\cdot)\)	1170.cl	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1170}(19,\cdot)\)	1170.ct	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1170}(23,\cdot)\)	1170.cm	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(i\)
\(\chi_{1170}(29,\cdot)\)	1170.bl	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(31,\cdot)\)	1170.cq	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(37,\cdot)\)	1170.cf	12	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1170}(41,\cdot)\)	1170.cx	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(-1\)
\(\chi_{1170}(43,\cdot)\)	1170.di	12	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(i\)
\(\chi_{1170}(47,\cdot)\)	1170.ce	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1170}(49,\cdot)\)	1170.bz	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)
\(\chi_{1170}(53,\cdot)\)	1170.o	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{1170}(59,\cdot)\)	1170.da	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1170}(61,\cdot)\)	1170.l	3	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)
\(\chi_{1170}(67,\cdot)\)	1170.cb	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(i\)
\(\chi_{1170}(71,\cdot)\)	1170.cu	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1170}(73,\cdot)\)	1170.m	4	no	\(1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(-i\)
\(\chi_{1170}(77,\cdot)\)	1170.cp	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1170}(79,\cdot)\)	1170.bo	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1170}(83,\cdot)\)	1170.ce	12	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1170}(89,\cdot)\)	1170.dc	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1170}(97,\cdot)\)	1170.cb	12	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(i\)
\(\chi_{1170}(101,\cdot)\)	1170.bw	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1170}(103,\cdot)\)	1170.dl	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{1170}(107,\cdot)\)	1170.dk	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1170}(109,\cdot)\)	1170.t	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-i\)	\(1\)
\(\chi_{1170}(113,\cdot)\)	1170.cj	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1170}(119,\cdot)\)	1170.da	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1170}(121,\cdot)\)	1170.bm	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1170}(127,\cdot)\)	1170.dh	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)

Introduction

L-functions

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First 32 of 288 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.