LMFDB - Group of Dirichlet characters of modulus 1665

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1665)

pari: g = idealstar(,1665,2)

Character group

sage: G.order() pari: g.no
Order	=	864
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{12}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1665}(371,\cdot)$, $\chi_{1665}(667,\cdot)$, $\chi_{1665}(631,\cdot)$

First 32 of 864 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1665}(1,\cdot)$	1665.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1665}(2,\cdot)$	1665.ez	36	yes	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{18}\right)$	$i$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{1665}(4,\cdot)$	1665.eh	18	yes	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{7}{9}\right)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1665}(7,\cdot)$	1665.fk	36	yes	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{1665}(8,\cdot)$	1665.ck	12	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1665}(11,\cdot)$	1665.bx	6	no	$-1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{1665}(13,\cdot)$	1665.fy	36	yes	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$i$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{1665}(14,\cdot)$	1665.cr	12	yes	$1$	$1$	$i$	$-1$	$e\left(\frac{1}{6}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1665}(16,\cdot)$	1665.cc	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1665}(17,\cdot)$	1665.ga	36	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{1665}(19,\cdot)$	1665.fo	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{1665}(22,\cdot)$	1665.ex	36	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{1665}(23,\cdot)$	1665.dx	12	yes	$-1$	$1$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1665}(26,\cdot)$	1665.bn	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1665}(28,\cdot)$	1665.fe	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1665}(29,\cdot)$	1665.cr	12	yes	$1$	$1$	$i$	$-1$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1665}(31,\cdot)$	1665.cx	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$-i$
$\chi_{1665}(32,\cdot)$	1665.ez	36	yes	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{17}{18}\right)$	$i$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{1665}(34,\cdot)$	1665.ek	18	yes	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1665}(38,\cdot)$	1665.df	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$-1$
$\chi_{1665}(41,\cdot)$	1665.ea	18	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{1665}(43,\cdot)$	1665.dv	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$-i$
$\chi_{1665}(44,\cdot)$	1665.eg	18	no	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1665}(46,\cdot)$	1665.cb	9	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1665}(47,\cdot)$	1665.dg	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1665}(49,\cdot)$	1665.ek	18	yes	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1665}(52,\cdot)$	1665.fy	36	yes	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{18}\right)$	$-i$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{1665}(53,\cdot)$	1665.fn	36	no	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{1665}(56,\cdot)$	1665.fi	36	no	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{1665}(58,\cdot)$	1665.ff	36	yes	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1665}(59,\cdot)$	1665.fh	36	yes	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{1665}(61,\cdot)$	1665.fp	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$

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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	$1665$
Structure	\(C_{2}\times C_{12}\times C_{36}\)
Order	$864$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1665}(1,\cdot)\)	1665.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1665}(2,\cdot)\)	1665.ez	36	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(i\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{1665}(4,\cdot)\)	1665.eh	18	yes	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1665}(7,\cdot)\)	1665.fk	36	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{1665}(8,\cdot)\)	1665.ck	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1665}(11,\cdot)\)	1665.bx	6	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{1665}(13,\cdot)\)	1665.fy	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)	\(i\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{1665}(14,\cdot)\)	1665.cr	12	yes	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1665}(16,\cdot)\)	1665.cc	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1665}(17,\cdot)\)	1665.ga	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{1665}(19,\cdot)\)	1665.fo	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{1665}(22,\cdot)\)	1665.ex	36	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{1665}(23,\cdot)\)	1665.dx	12	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1665}(26,\cdot)\)	1665.bn	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1665}(28,\cdot)\)	1665.fe	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1665}(29,\cdot)\)	1665.cr	12	yes	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1665}(31,\cdot)\)	1665.cx	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(-i\)
\(\chi_{1665}(32,\cdot)\)	1665.ez	36	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(i\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{1665}(34,\cdot)\)	1665.ek	18	yes	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1665}(38,\cdot)\)	1665.df	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(-1\)
\(\chi_{1665}(41,\cdot)\)	1665.ea	18	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{1665}(43,\cdot)\)	1665.dv	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(-i\)
\(\chi_{1665}(44,\cdot)\)	1665.eg	18	no	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1665}(46,\cdot)\)	1665.cb	9	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1665}(47,\cdot)\)	1665.dg	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1665}(49,\cdot)\)	1665.ek	18	yes	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1665}(52,\cdot)\)	1665.fy	36	yes	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{18}\right)\)	\(-i\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{1665}(53,\cdot)\)	1665.fn	36	no	\(1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{1665}(56,\cdot)\)	1665.fi	36	no	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{1665}(58,\cdot)\)	1665.ff	36	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1665}(59,\cdot)\)	1665.fh	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{1665}(61,\cdot)\)	1665.fp	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.