LMFDB - Group of Dirichlet characters of modulus 945

Show commands: PariGP / SageMath

sage: H = DirichletGroup(945)

pari: g = idealstar(,945,2)

Character group

sage: G.order() pari: g.no
Order	=	432
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{945}(596,\cdot)$, $\chi_{945}(757,\cdot)$, $\chi_{945}(136,\cdot)$

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	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{945}(1,\cdot)$	945.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{945}(2,\cdot)$	945.do	36	yes	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{945}(4,\cdot)$	945.db	18	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{945}(8,\cdot)$	945.cf	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{945}(11,\cdot)$	945.cv	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{945}(13,\cdot)$	945.di	36	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{945}(16,\cdot)$	945.bs	9	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{945}(17,\cdot)$	945.bz	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$-1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{945}(19,\cdot)$	945.bn	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{945}(22,\cdot)$	945.dp	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{945}(23,\cdot)$	945.dh	36	yes	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{9}\right)$	$i$	$-1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{945}(26,\cdot)$	945.bj	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{945}(29,\cdot)$	945.cn	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{945}(31,\cdot)$	945.cr	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{945}(32,\cdot)$	945.do	36	yes	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{945}(34,\cdot)$	945.cw	18	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{945}(37,\cdot)$	945.bw	12	no	$-1$	$1$	$i$	$-1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{945}(38,\cdot)$	945.dq	36	yes	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{9}\right)$	$-i$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{945}(41,\cdot)$	945.cz	18	no	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{945}(43,\cdot)$	945.dp	36	no	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{945}(44,\cdot)$	945.br	6	no	$-1$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{945}(46,\cdot)$	945.l	3	no	$1$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{945}(47,\cdot)$	945.dj	36	yes	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{945}(52,\cdot)$	945.dr	36	yes	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{9}\right)$	$-i$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{945}(53,\cdot)$	945.ch	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{12}\right)$
$\chi_{945}(58,\cdot)$	945.dg	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{9}\right)$	$-i$	$-1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{945}(59,\cdot)$	945.cq	18	yes	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{945}(61,\cdot)$	945.cr	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{945}(62,\cdot)$	945.ci	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{945}(64,\cdot)$	945.bh	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{945}(67,\cdot)$	945.dn	36	yes	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{945}(68,\cdot)$	945.dq	36	yes	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{9}\right)$	$-i$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{36}\right)$

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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	$945$
Structure	\(C_{2}\times C_{6}\times C_{36}\)
Order	$432$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)	\(22\)	\(23\)
\(\chi_{945}(1,\cdot)\)	945.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{945}(2,\cdot)\)	945.do	36	yes	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{945}(4,\cdot)\)	945.db	18	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{945}(8,\cdot)\)	945.cf	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{945}(11,\cdot)\)	945.cv	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{945}(13,\cdot)\)	945.di	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{945}(16,\cdot)\)	945.bs	9	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{945}(17,\cdot)\)	945.bz	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{945}(19,\cdot)\)	945.bn	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{945}(22,\cdot)\)	945.dp	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{945}(23,\cdot)\)	945.dh	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{945}(26,\cdot)\)	945.bj	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{945}(29,\cdot)\)	945.cn	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{945}(31,\cdot)\)	945.cr	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{945}(32,\cdot)\)	945.do	36	yes	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{945}(34,\cdot)\)	945.cw	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{945}(37,\cdot)\)	945.bw	12	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{945}(38,\cdot)\)	945.dq	36	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{945}(41,\cdot)\)	945.cz	18	no	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{945}(43,\cdot)\)	945.dp	36	no	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{945}(44,\cdot)\)	945.br	6	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{945}(46,\cdot)\)	945.l	3	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{945}(47,\cdot)\)	945.dj	36	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{945}(52,\cdot)\)	945.dr	36	yes	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{945}(53,\cdot)\)	945.ch	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{945}(58,\cdot)\)	945.dg	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{945}(59,\cdot)\)	945.cq	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{945}(61,\cdot)\)	945.cr	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{945}(62,\cdot)\)	945.ci	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{945}(64,\cdot)\)	945.bh	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{945}(67,\cdot)\)	945.dn	36	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{945}(68,\cdot)\)	945.dq	36	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)

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L-functions

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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.