LMFDB - Group of Dirichlet characters of modulus 153

Show commands: PariGP / SageMath

sage: H = DirichletGroup(153)

pari: g = idealstar(,153,2)

Character group

sage: G.order() pari: g.no
Order	=	96
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{48}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{153}(137,\cdot)$, $\chi_{153}(37,\cdot)$

First 32 of 96 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{153}(1,\cdot)$	153.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{153}(2,\cdot)$	153.q	24	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{153}(4,\cdot)$	153.n	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{153}(5,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(7,\cdot)$	153.t	48	yes	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{153}(8,\cdot)$	153.k	8	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{153}(10,\cdot)$	153.p	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{153}(11,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{153}(13,\cdot)$	153.n	12	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{153}(14,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(16,\cdot)$	153.h	6	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{153}(19,\cdot)$	153.l	8	no	$1$	$1$	$i$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{153}(20,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{153}(22,\cdot)$	153.t	48	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(23,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(25,\cdot)$	153.r	24	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{153}(26,\cdot)$	153.k	8	no	$-1$	$1$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{153}(28,\cdot)$	153.p	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$-1$
$\chi_{153}(29,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{153}(31,\cdot)$	153.t	48	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(32,\cdot)$	153.q	24	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{153}(35,\cdot)$	153.b	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{153}(37,\cdot)$	153.p	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{153}(38,\cdot)$	153.m	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$1$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{153}(40,\cdot)$	153.t	48	yes	$-1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(41,\cdot)$	153.s	48	yes	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{153}(43,\cdot)$	153.r	24	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{24}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{153}(44,\cdot)$	153.o	16	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{153}(46,\cdot)$	153.p	16	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{153}(47,\cdot)$	153.m	12	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{153}(49,\cdot)$	153.r	24	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{24}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{153}(50,\cdot)$	153.i	6	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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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	$153$
Structure	\(C_{2}\times C_{48}\)
Order	$96$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{153}(1,\cdot)\)	153.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{153}(2,\cdot)\)	153.q	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{153}(4,\cdot)\)	153.n	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{153}(5,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(7,\cdot)\)	153.t	48	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{153}(8,\cdot)\)	153.k	8	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{153}(10,\cdot)\)	153.p	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{153}(11,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{153}(13,\cdot)\)	153.n	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{153}(14,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(16,\cdot)\)	153.h	6	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{153}(19,\cdot)\)	153.l	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{153}(20,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{153}(22,\cdot)\)	153.t	48	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(23,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(25,\cdot)\)	153.r	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{153}(26,\cdot)\)	153.k	8	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{153}(28,\cdot)\)	153.p	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)
\(\chi_{153}(29,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{153}(31,\cdot)\)	153.t	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(32,\cdot)\)	153.q	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{153}(35,\cdot)\)	153.b	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{153}(37,\cdot)\)	153.p	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{153}(38,\cdot)\)	153.m	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{153}(40,\cdot)\)	153.t	48	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(41,\cdot)\)	153.s	48	yes	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{153}(43,\cdot)\)	153.r	24	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{153}(44,\cdot)\)	153.o	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{153}(46,\cdot)\)	153.p	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{153}(47,\cdot)\)	153.m	12	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{153}(49,\cdot)\)	153.r	24	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{153}(50,\cdot)\)	153.i	6	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.