LMFDB - Group of Dirichlet characters of modulus 388

Show commands: PariGP / SageMath

sage: H = DirichletGroup(388)

pari: g = idealstar(,388,2)

Character group

sage: G.order() pari: g.no
Order	=	192
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{96}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{388}(195,\cdot)$, $\chi_{388}(5,\cdot)$

First 32 of 192 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{388}(1,\cdot)$	388.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{388}(3,\cdot)$	388.v	48	yes	$-1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{388}(5,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{96}\right)$
$\chi_{388}(7,\cdot)$	388.x	96	yes	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{59}{96}\right)$
$\chi_{388}(9,\cdot)$	388.q	24	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{388}(11,\cdot)$	388.v	48	yes	$-1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{388}(13,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{29}{96}\right)$
$\chi_{388}(15,\cdot)$	388.x	96	yes	$1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{388}(17,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{61}{96}\right)$
$\chi_{388}(19,\cdot)$	388.s	32	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{388}(21,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{25}{96}\right)$
$\chi_{388}(23,\cdot)$	388.x	96	yes	$1$	$1$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{96}\right)$
$\chi_{388}(25,\cdot)$	388.u	48	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{388}(27,\cdot)$	388.o	16	yes	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{388}(29,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{65}{96}\right)$
$\chi_{388}(31,\cdot)$	388.v	48	yes	$-1$	$1$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{388}(33,\cdot)$	388.l	8	no	$1$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{388}(35,\cdot)$	388.i	6	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{388}(37,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{71}{96}\right)$
$\chi_{388}(39,\cdot)$	388.x	96	yes	$1$	$1$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{91}{96}\right)$
$\chi_{388}(41,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{41}{96}\right)$
$\chi_{388}(43,\cdot)$	388.r	24	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{388}(45,\cdot)$	388.t	32	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{388}(47,\cdot)$	388.k	8	yes	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{388}(49,\cdot)$	388.u	48	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{388}(51,\cdot)$	388.s	32	yes	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{388}(53,\cdot)$	388.u	48	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{388}(55,\cdot)$	388.s	32	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{388}(57,\cdot)$	388.w	96	no	$-1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{83}{96}\right)$
$\chi_{388}(59,\cdot)$	388.x	96	yes	$1$	$1$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{388}(61,\cdot)$	388.e	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{388}(63,\cdot)$	388.s	32	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{29}{32}\right)$

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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 $\F_{q}$

Modulus	$388$
Structure	\(C_{2}\times C_{96}\)
Order	$192$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{388}(1,\cdot)\)	388.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{388}(3,\cdot)\)	388.v	48	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{388}(5,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{96}\right)\)
\(\chi_{388}(7,\cdot)\)	388.x	96	yes	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{59}{96}\right)\)
\(\chi_{388}(9,\cdot)\)	388.q	24	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{388}(11,\cdot)\)	388.v	48	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{388}(13,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{29}{96}\right)\)
\(\chi_{388}(15,\cdot)\)	388.x	96	yes	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{388}(17,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{61}{96}\right)\)
\(\chi_{388}(19,\cdot)\)	388.s	32	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{388}(21,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{25}{96}\right)\)
\(\chi_{388}(23,\cdot)\)	388.x	96	yes	\(1\)	\(1\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{96}\right)\)
\(\chi_{388}(25,\cdot)\)	388.u	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{388}(27,\cdot)\)	388.o	16	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{388}(29,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{65}{96}\right)\)
\(\chi_{388}(31,\cdot)\)	388.v	48	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{388}(33,\cdot)\)	388.l	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{388}(35,\cdot)\)	388.i	6	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{388}(37,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{71}{96}\right)\)
\(\chi_{388}(39,\cdot)\)	388.x	96	yes	\(1\)	\(1\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{388}(41,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{41}{96}\right)\)
\(\chi_{388}(43,\cdot)\)	388.r	24	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{388}(45,\cdot)\)	388.t	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{388}(47,\cdot)\)	388.k	8	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{388}(49,\cdot)\)	388.u	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{388}(51,\cdot)\)	388.s	32	yes	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{388}(53,\cdot)\)	388.u	48	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{388}(55,\cdot)\)	388.s	32	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{388}(57,\cdot)\)	388.w	96	no	\(-1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{83}{96}\right)\)
\(\chi_{388}(59,\cdot)\)	388.x	96	yes	\(1\)	\(1\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{388}(61,\cdot)\)	388.e	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{388}(63,\cdot)\)	388.s	32	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)

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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.