LMFDB - Group of Dirichlet characters of modulus 3328

sage:H = DirichletGroup(3328)

pari:g = idealstar(,3328,2)

Character group

sage:G.order() pari:g.no
Order	=	1536
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{192}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{3328}(1535,\cdot)$, $\chi_{3328}(261,\cdot)$, $\chi_{3328}(769,\cdot)$

First 32 of 1536 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{3328}(1,\cdot)$	3328.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3328}(3,\cdot)$	3328.du	192	yes	$-1$	$1$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{3328}(5,\cdot)$	3328.dd	64	yes	$-1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{23}{32}\right)$
$\chi_{3328}(7,\cdot)$	3328.dr	96	no	$1$	$1$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{3328}(9,\cdot)$	3328.do	96	no	$1$	$1$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{3328}(11,\cdot)$	3328.dz	192	yes	$1$	$1$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{89}{96}\right)$
$\chi_{3328}(15,\cdot)$	3328.db	48	no	$1$	$1$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{3328}(17,\cdot)$	3328.cy	48	no	$1$	$1$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{3328}(19,\cdot)$	3328.dz	192	yes	$1$	$1$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{3328}(21,\cdot)$	3328.dj	64	yes	$-1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3328}(23,\cdot)$	3328.dp	96	no	$-1$	$1$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{3328}(25,\cdot)$	3328.cr	32	no	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{3328}(27,\cdot)$	3328.dg	64	no	$-1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{3328}(29,\cdot)$	3328.dx	192	yes	$1$	$1$	$e\left(\frac{115}{192}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{23}{96}\right)$
$\chi_{3328}(31,\cdot)$	3328.bi	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-i$	$e\left(\frac{3}{8}\right)$	$-i$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{3328}(33,\cdot)$	3328.cl	24	no	$-1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{3328}(35,\cdot)$	3328.du	192	yes	$-1$	$1$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{55}{96}\right)$
$\chi_{3328}(37,\cdot)$	3328.ds	192	yes	$-1$	$1$	$e\left(\frac{1}{192}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{29}{96}\right)$
$\chi_{3328}(41,\cdot)$	3328.dl	96	no	$-1$	$1$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{3328}(43,\cdot)$	3328.dv	192	yes	$-1$	$1$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{49}{96}\right)$
$\chi_{3328}(45,\cdot)$	3328.ds	192	yes	$-1$	$1$	$e\left(\frac{95}{192}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{115}{192}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{67}{96}\right)$
$\chi_{3328}(47,\cdot)$	3328.bw	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{3328}(49,\cdot)$	3328.cy	48	no	$1$	$1$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{3328}(51,\cdot)$	3328.dh	64	yes	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3328}(53,\cdot)$	3328.df	64	no	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3328}(55,\cdot)$	3328.dn	96	no	$-1$	$1$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{3328}(57,\cdot)$	3328.ct	32	no	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{3328}(59,\cdot)$	3328.dz	192	yes	$1$	$1$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{95}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{37}{96}\right)$
$\chi_{3328}(61,\cdot)$	3328.dx	192	yes	$1$	$1$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{79}{96}\right)$
$\chi_{3328}(63,\cdot)$	3328.bn	12	no	$1$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{3328}(67,\cdot)$	3328.dz	192	yes	$1$	$1$	$e\left(\frac{139}{192}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{47}{96}\right)$
$\chi_{3328}(69,\cdot)$	3328.dw	192	yes	$1$	$1$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{37}{96}\right)$

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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	$3328$
Structure	\(C_{2}\times C_{4}\times C_{192}\)
Order	$1536$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{3328}(1,\cdot)\)	3328.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3328}(3,\cdot)\)	3328.du	192	yes	\(-1\)	\(1\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{3328}(5,\cdot)\)	3328.dd	64	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)
\(\chi_{3328}(7,\cdot)\)	3328.dr	96	no	\(1\)	\(1\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{3328}(9,\cdot)\)	3328.do	96	no	\(1\)	\(1\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{3328}(11,\cdot)\)	3328.dz	192	yes	\(1\)	\(1\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{89}{96}\right)\)
\(\chi_{3328}(15,\cdot)\)	3328.db	48	no	\(1\)	\(1\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{3328}(17,\cdot)\)	3328.cy	48	no	\(1\)	\(1\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{3328}(19,\cdot)\)	3328.dz	192	yes	\(1\)	\(1\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{3328}(21,\cdot)\)	3328.dj	64	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3328}(23,\cdot)\)	3328.dp	96	no	\(-1\)	\(1\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{3328}(25,\cdot)\)	3328.cr	32	no	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{3328}(27,\cdot)\)	3328.dg	64	no	\(-1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{3328}(29,\cdot)\)	3328.dx	192	yes	\(1\)	\(1\)	\(e\left(\frac{115}{192}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{23}{96}\right)\)
\(\chi_{3328}(31,\cdot)\)	3328.bi	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{3328}(33,\cdot)\)	3328.cl	24	no	\(-1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{3328}(35,\cdot)\)	3328.du	192	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{55}{96}\right)\)
\(\chi_{3328}(37,\cdot)\)	3328.ds	192	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{192}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)
\(\chi_{3328}(41,\cdot)\)	3328.dl	96	no	\(-1\)	\(1\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{3328}(43,\cdot)\)	3328.dv	192	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{49}{96}\right)\)
\(\chi_{3328}(45,\cdot)\)	3328.ds	192	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{192}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{115}{192}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{67}{96}\right)\)
\(\chi_{3328}(47,\cdot)\)	3328.bw	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3328}(49,\cdot)\)	3328.cy	48	no	\(1\)	\(1\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{3328}(51,\cdot)\)	3328.dh	64	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3328}(53,\cdot)\)	3328.df	64	no	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3328}(55,\cdot)\)	3328.dn	96	no	\(-1\)	\(1\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{3328}(57,\cdot)\)	3328.ct	32	no	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{3328}(59,\cdot)\)	3328.dz	192	yes	\(1\)	\(1\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{95}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)
\(\chi_{3328}(61,\cdot)\)	3328.dx	192	yes	\(1\)	\(1\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{3328}(63,\cdot)\)	3328.bn	12	no	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3328}(67,\cdot)\)	3328.dz	192	yes	\(1\)	\(1\)	\(e\left(\frac{139}{192}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)
\(\chi_{3328}(69,\cdot)\)	3328.dw	192	yes	\(1\)	\(1\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)

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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.