LMFDB - Group of Dirichlet characters of modulus 3840

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3840)

pari: g = idealstar(,3840,2)

Character group

sage: G.order() pari: g.no
Order	=	1024
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{64}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3840}(511,\cdot)$, $\chi_{3840}(2821,\cdot)$, $\chi_{3840}(2561,\cdot)$, $\chi_{3840}(1537,\cdot)$

First 32 of 1024 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{3840}(1,\cdot)$	3840.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3840}(7,\cdot)$	3840.cx	32	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{32}\right)$	$-i$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{3840}(11,\cdot)$	3840.dw	64	no	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{3840}(13,\cdot)$	3840.du	64	no	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3840}(17,\cdot)$	3840.cr	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{3840}(19,\cdot)$	3840.dk	64	no	$-1$	$1$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3840}(23,\cdot)$	3840.cv	32	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{32}\right)$	$i$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{3840}(29,\cdot)$	3840.dy	64	yes	$-1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{3840}(31,\cdot)$	3840.bt	8	no	$-1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{3840}(37,\cdot)$	3840.du	64	no	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3840}(41,\cdot)$	3840.de	32	no	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{21}{32}\right)$	$-i$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{3840}(43,\cdot)$	3840.do	64	no	$1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3840}(47,\cdot)$	3840.ct	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{3840}(49,\cdot)$	3840.ck	16	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{3840}(53,\cdot)$	3840.dr	64	yes	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{11}{32}\right)$
$\chi_{3840}(59,\cdot)$	3840.dn	64	yes	$1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{31}{32}\right)$
$\chi_{3840}(61,\cdot)$	3840.dm	64	no	$1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3840}(67,\cdot)$	3840.do	64	no	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3840}(71,\cdot)$	3840.cy	32	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{32}\right)$	$-i$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{3840}(73,\cdot)$	3840.cu	32	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{32}\right)$	$-i$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{3840}(77,\cdot)$	3840.dr	64	yes	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{17}{32}\right)$
$\chi_{3840}(79,\cdot)$	3840.co	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{3840}(83,\cdot)$	3840.dt	64	yes	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3840}(89,\cdot)$	3840.db	32	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{19}{32}\right)$	$i$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{3840}(91,\cdot)$	3840.dz	64	no	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3840}(97,\cdot)$	3840.bp	8	no	$-1$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$
$\chi_{3840}(101,\cdot)$	3840.dl	64	no	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3840}(103,\cdot)$	3840.di	32	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{27}{32}\right)$	$-i$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{3840}(107,\cdot)$	3840.dt	64	yes	$-1$	$1$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{3}{32}\right)$
$\chi_{3840}(109,\cdot)$	3840.dx	64	no	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{9}{32}\right)$
$\chi_{3840}(113,\cdot)$	3840.cr	16	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{3840}(119,\cdot)$	3840.dd	32	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{32}\right)$	$i$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{16}\right)$

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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	$3840$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{64}\)
Order	$1024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{3840}(1,\cdot)\)	3840.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3840}(7,\cdot)\)	3840.cx	32	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(-i\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{3840}(11,\cdot)\)	3840.dw	64	no	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{3840}(13,\cdot)\)	3840.du	64	no	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3840}(17,\cdot)\)	3840.cr	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{3840}(19,\cdot)\)	3840.dk	64	no	\(-1\)	\(1\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3840}(23,\cdot)\)	3840.cv	32	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(i\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{3840}(29,\cdot)\)	3840.dy	64	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{3840}(31,\cdot)\)	3840.bt	8	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{3840}(37,\cdot)\)	3840.du	64	no	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3840}(41,\cdot)\)	3840.de	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(-i\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{3840}(43,\cdot)\)	3840.do	64	no	\(1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3840}(47,\cdot)\)	3840.ct	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3840}(49,\cdot)\)	3840.ck	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3840}(53,\cdot)\)	3840.dr	64	yes	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{3840}(59,\cdot)\)	3840.dn	64	yes	\(1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)
\(\chi_{3840}(61,\cdot)\)	3840.dm	64	no	\(1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3840}(67,\cdot)\)	3840.do	64	no	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3840}(71,\cdot)\)	3840.cy	32	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(-i\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{3840}(73,\cdot)\)	3840.cu	32	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(-i\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{3840}(77,\cdot)\)	3840.dr	64	yes	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)
\(\chi_{3840}(79,\cdot)\)	3840.co	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3840}(83,\cdot)\)	3840.dt	64	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3840}(89,\cdot)\)	3840.db	32	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(i\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{3840}(91,\cdot)\)	3840.dz	64	no	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3840}(97,\cdot)\)	3840.bp	8	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)
\(\chi_{3840}(101,\cdot)\)	3840.dl	64	no	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3840}(103,\cdot)\)	3840.di	32	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(-i\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{3840}(107,\cdot)\)	3840.dt	64	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)
\(\chi_{3840}(109,\cdot)\)	3840.dx	64	no	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{3840}(113,\cdot)\)	3840.cr	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{3840}(119,\cdot)\)	3840.dd	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(i\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)

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L-functions

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Character group

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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.