LMFDB - Group of Dirichlet characters of modulus 1455

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1455)

gp:g = idealstar(,1455,2)

magma:G = FullDirichletGroup(1455);

Character group

Order	=	768	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{96}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1455}(971,\cdot)$, $\chi_{1455}(292,\cdot)$, $\chi_{1455}(781,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 768 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{1455}(1,\cdot)$	1455.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1455}(2,\cdot)$	1455.cy	48	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1455}(4,\cdot)$	1455.ch	24	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1455}(7,\cdot)$	1455.di	96	no	$1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{1455}(8,\cdot)$	1455.by	16	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1455}(11,\cdot)$	1455.cv	48	no	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1455}(13,\cdot)$	1455.di	96	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{1455}(14,\cdot)$	1455.dg	96	yes	$1$	$1$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{1455}(16,\cdot)$	1455.bv	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{1455}(17,\cdot)$	1455.dc	96	yes	$-1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{1455}(19,\cdot)$	1455.cr	32	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{27}{32}\right)$	$-i$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{1455}(22,\cdot)$	1455.r	4	no	$-1$	$1$	$-i$	$-1$	$1$	$i$	$-1$	$1$	$-i$	$1$	$-1$	$-i$
$\chi_{1455}(23,\cdot)$	1455.dj	96	yes	$-1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{1455}(26,\cdot)$	1455.df	96	no	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{1455}(28,\cdot)$	1455.cm	32	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{17}{32}\right)$	$i$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{1455}(29,\cdot)$	1455.dg	96	yes	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{1455}(31,\cdot)$	1455.cu	48	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1455}(32,\cdot)$	1455.cy	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1455}(34,\cdot)$	1455.cr	32	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{9}{32}\right)$	$i$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{1455}(37,\cdot)$	1455.di	96	no	$1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{1455}(38,\cdot)$	1455.dc	96	yes	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{1455}(41,\cdot)$	1455.df	96	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{1455}(43,\cdot)$	1455.cl	24	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{24}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1455}(44,\cdot)$	1455.da	48	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1455}(46,\cdot)$	1455.co	32	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{5}{32}\right)$	$i$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{1455}(47,\cdot)$	1455.bd	8	yes	$1$	$1$	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1455}(49,\cdot)$	1455.db	48	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1455}(52,\cdot)$	1455.cm	32	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{32}\right)$	$-i$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{1455}(53,\cdot)$	1455.cx	48	yes	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1455}(56,\cdot)$	1455.df	96	no	$1$	$1$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{1455}(58,\cdot)$	1455.dd	96	no	$1$	$1$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{1455}(59,\cdot)$	1455.dg	96	yes	$1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{17}{32}\right)$

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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	$1455$
Structure	\(C_{2}\times C_{4}\times C_{96}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{1455}(1,\cdot)\)	1455.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1455}(2,\cdot)\)	1455.cy	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1455}(4,\cdot)\)	1455.ch	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1455}(7,\cdot)\)	1455.di	96	no	\(1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{1455}(8,\cdot)\)	1455.by	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1455}(11,\cdot)\)	1455.cv	48	no	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1455}(13,\cdot)\)	1455.di	96	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{1455}(14,\cdot)\)	1455.dg	96	yes	\(1\)	\(1\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{1455}(16,\cdot)\)	1455.bv	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)
\(\chi_{1455}(17,\cdot)\)	1455.dc	96	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{1455}(19,\cdot)\)	1455.cr	32	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(-i\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{1455}(22,\cdot)\)	1455.r	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)
\(\chi_{1455}(23,\cdot)\)	1455.dj	96	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{1455}(26,\cdot)\)	1455.df	96	no	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{1455}(28,\cdot)\)	1455.cm	32	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(i\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{1455}(29,\cdot)\)	1455.dg	96	yes	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{1455}(31,\cdot)\)	1455.cu	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1455}(32,\cdot)\)	1455.cy	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1455}(34,\cdot)\)	1455.cr	32	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(i\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{1455}(37,\cdot)\)	1455.di	96	no	\(1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{1455}(38,\cdot)\)	1455.dc	96	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{1455}(41,\cdot)\)	1455.df	96	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{1455}(43,\cdot)\)	1455.cl	24	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1455}(44,\cdot)\)	1455.da	48	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1455}(46,\cdot)\)	1455.co	32	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(i\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{1455}(47,\cdot)\)	1455.bd	8	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1455}(49,\cdot)\)	1455.db	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1455}(52,\cdot)\)	1455.cm	32	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(-i\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{1455}(53,\cdot)\)	1455.cx	48	yes	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1455}(56,\cdot)\)	1455.df	96	no	\(1\)	\(1\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{1455}(58,\cdot)\)	1455.dd	96	no	\(1\)	\(1\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{1455}(59,\cdot)\)	1455.dg	96	yes	\(1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)

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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.