LMFDB - Group of Dirichlet characters of modulus 459

sage:H = DirichletGroup(459)

pari:g = idealstar(,459,2)

Character group

sage:G.order() pari:g.no
Order	=	288
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{144}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{459}(137,\cdot)$, $\chi_{459}(190,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{459}(1,\cdot)$	459.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{459}(2,\cdot)$	459.bb	72	yes	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{459}(4,\cdot)$	459.x	36	yes	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{459}(5,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{459}(7,\cdot)$	459.bc	144	yes	$-1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{459}(8,\cdot)$	459.u	24	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{24}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{459}(10,\cdot)$	459.z	48	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{459}(11,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{459}(13,\cdot)$	459.x	36	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{459}(14,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{459}(16,\cdot)$	459.r	18	yes	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{459}(19,\cdot)$	459.v	24	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{24}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{459}(20,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{1}{18}\right)$
$\chi_{459}(22,\cdot)$	459.bc	144	yes	$-1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{11}{18}\right)$
$\chi_{459}(23,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{459}(25,\cdot)$	459.ba	72	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{459}(26,\cdot)$	459.k	8	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{459}(28,\cdot)$	459.q	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$-1$
$\chi_{459}(29,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{13}{18}\right)$
$\chi_{459}(31,\cdot)$	459.bc	144	yes	$-1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{459}(32,\cdot)$	459.bb	72	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{459}(35,\cdot)$	459.j	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{459}(37,\cdot)$	459.z	48	no	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{459}(38,\cdot)$	459.w	36	yes	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{459}(40,\cdot)$	459.bc	144	yes	$-1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{459}(41,\cdot)$	459.bd	144	yes	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{459}(43,\cdot)$	459.ba	72	yes	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{459}(44,\cdot)$	459.y	48	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{459}(46,\cdot)$	459.z	48	no	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{459}(47,\cdot)$	459.w	36	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{459}(49,\cdot)$	459.ba	72	yes	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{459}(50,\cdot)$	459.t	18	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$459$
Structure	\(C_{2}\times C_{144}\)
Order	$288$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{459}(1,\cdot)\)	459.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{459}(2,\cdot)\)	459.bb	72	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{459}(4,\cdot)\)	459.x	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{459}(5,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{459}(7,\cdot)\)	459.bc	144	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{459}(8,\cdot)\)	459.u	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{459}(10,\cdot)\)	459.z	48	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{459}(11,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{459}(13,\cdot)\)	459.x	36	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{459}(14,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{459}(16,\cdot)\)	459.r	18	yes	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{459}(19,\cdot)\)	459.v	24	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{459}(20,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{1}{18}\right)\)
\(\chi_{459}(22,\cdot)\)	459.bc	144	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{11}{18}\right)\)
\(\chi_{459}(23,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{459}(25,\cdot)\)	459.ba	72	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{459}(26,\cdot)\)	459.k	8	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{459}(28,\cdot)\)	459.q	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)
\(\chi_{459}(29,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{13}{18}\right)\)
\(\chi_{459}(31,\cdot)\)	459.bc	144	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{459}(32,\cdot)\)	459.bb	72	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{459}(35,\cdot)\)	459.j	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{459}(37,\cdot)\)	459.z	48	no	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{459}(38,\cdot)\)	459.w	36	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{459}(40,\cdot)\)	459.bc	144	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{459}(41,\cdot)\)	459.bd	144	yes	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{459}(43,\cdot)\)	459.ba	72	yes	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{459}(44,\cdot)\)	459.y	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{459}(46,\cdot)\)	459.z	48	no	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{459}(47,\cdot)\)	459.w	36	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{459}(49,\cdot)\)	459.ba	72	yes	\(1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{459}(50,\cdot)\)	459.t	18	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)

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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.