LMFDB - Group of Dirichlet characters of modulus 2160

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2160)

pari: g = idealstar(,2160,2)

Character group

sage: G.order() pari: g.no
Order	=	576
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2160}(271,\cdot)$, $\chi_{2160}(1621,\cdot)$, $\chi_{2160}(2081,\cdot)$, $\chi_{2160}(1297,\cdot)$

First 32 of 576 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2160}(1,\cdot)$	2160.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2160}(7,\cdot)$	2160.el	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2160}(11,\cdot)$	2160.ep	36	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2160}(13,\cdot)$	2160.eh	36	yes	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2160}(17,\cdot)$	2160.cv	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{2160}(19,\cdot)$	2160.da	12	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{2160}(23,\cdot)$	2160.ei	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{2160}(29,\cdot)$	2160.ds	36	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2160}(31,\cdot)$	2160.dh	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{2160}(37,\cdot)$	2160.cs	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{2160}(41,\cdot)$	2160.dr	18	no	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2160}(43,\cdot)$	2160.ea	36	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{2160}(47,\cdot)$	2160.dw	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2160}(49,\cdot)$	2160.dm	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2160}(53,\cdot)$	2160.bg	4	no	$1$	$1$	$i$	$-i$	$1$	$i$	$i$	$i$	$-i$	$1$	$1$	$1$
$\chi_{2160}(59,\cdot)$	2160.du	36	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2160}(61,\cdot)$	2160.dv	36	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{2160}(67,\cdot)$	2160.ea	36	yes	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{2160}(71,\cdot)$	2160.cc	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{2160}(73,\cdot)$	2160.cx	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{2160}(77,\cdot)$	2160.ec	36	yes	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{2160}(79,\cdot)$	2160.dq	18	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2160}(83,\cdot)$	2160.ef	36	yes	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{2160}(89,\cdot)$	2160.bx	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{2160}(91,\cdot)$	2160.ch	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{2160}(97,\cdot)$	2160.ej	36	no	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{2160}(101,\cdot)$	2160.en	36	no	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{2160}(103,\cdot)$	2160.el	36	no	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{2160}(107,\cdot)$	2160.ba	4	no	$-1$	$1$	$i$	$i$	$-1$	$-i$	$-i$	$i$	$-i$	$-1$	$-1$	$1$
$\chi_{2160}(109,\cdot)$	2160.bm	4	no	$1$	$1$	$1$	$-i$	$-i$	$-1$	$i$	$1$	$i$	$1$	$i$	$-1$
$\chi_{2160}(113,\cdot)$	2160.ek	36	no	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{2160}(119,\cdot)$	2160.dd	18	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$

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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	$2160$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{36}\)
Order	$576$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2160}(1,\cdot)\)	2160.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2160}(7,\cdot)\)	2160.el	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2160}(11,\cdot)\)	2160.ep	36	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2160}(13,\cdot)\)	2160.eh	36	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2160}(17,\cdot)\)	2160.cv	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2160}(19,\cdot)\)	2160.da	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2160}(23,\cdot)\)	2160.ei	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{2160}(29,\cdot)\)	2160.ds	36	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2160}(31,\cdot)\)	2160.dh	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{2160}(37,\cdot)\)	2160.cs	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2160}(41,\cdot)\)	2160.dr	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2160}(43,\cdot)\)	2160.ea	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{2160}(47,\cdot)\)	2160.dw	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2160}(49,\cdot)\)	2160.dm	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2160}(53,\cdot)\)	2160.bg	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(1\)
\(\chi_{2160}(59,\cdot)\)	2160.du	36	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2160}(61,\cdot)\)	2160.dv	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{2160}(67,\cdot)\)	2160.ea	36	yes	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{2160}(71,\cdot)\)	2160.cc	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2160}(73,\cdot)\)	2160.cx	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2160}(77,\cdot)\)	2160.ec	36	yes	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{2160}(79,\cdot)\)	2160.dq	18	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2160}(83,\cdot)\)	2160.ef	36	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{2160}(89,\cdot)\)	2160.bx	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2160}(91,\cdot)\)	2160.ch	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2160}(97,\cdot)\)	2160.ej	36	no	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{2160}(101,\cdot)\)	2160.en	36	no	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{2160}(103,\cdot)\)	2160.el	36	no	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{2160}(107,\cdot)\)	2160.ba	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-i\)	\(-i\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{2160}(109,\cdot)\)	2160.bm	4	no	\(1\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(i\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-1\)
\(\chi_{2160}(113,\cdot)\)	2160.ek	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{2160}(119,\cdot)\)	2160.dd	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)

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L-functions

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First 32 of 576 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.