LMFDB - Group of Dirichlet characters of modulus 6400

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6400)

pari: g = idealstar(,6400,2)

Character group

sage: G.order() pari: g.no
Order	=	2560
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{320}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6400}(4351,\cdot)$, $\chi_{6400}(4101,\cdot)$, $\chi_{6400}(5377,\cdot)$

First 32 of 2560 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{6400}(1,\cdot)$	6400.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6400}(3,\cdot)$	6400.dz	320	yes	$1$	$1$	$e\left(\frac{29}{320}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{187}{320}\right)$	$e\left(\frac{113}{320}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{121}{320}\right)$	$e\left(\frac{259}{320}\right)$	$e\left(\frac{1}{160}\right)$	$e\left(\frac{87}{320}\right)$
$\chi_{6400}(7,\cdot)$	6400.cf	32	no	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{6400}(9,\cdot)$	6400.dn	160	no	$1$	$1$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{87}{160}\right)$
$\chi_{6400}(11,\cdot)$	6400.dv	320	yes	$-1$	$1$	$e\left(\frac{187}{320}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{61}{320}\right)$	$e\left(\frac{199}{320}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{143}{320}\right)$	$e\left(\frac{117}{320}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{241}{320}\right)$
$\chi_{6400}(13,\cdot)$	6400.dt	320	yes	$-1$	$1$	$e\left(\frac{113}{320}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{199}{320}\right)$	$e\left(\frac{181}{320}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{317}{320}\right)$	$e\left(\frac{143}{320}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{19}{320}\right)$
$\chi_{6400}(17,\cdot)$	6400.dj	80	no	$-1$	$1$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{6400}(19,\cdot)$	6400.dw	320	yes	$-1$	$1$	$e\left(\frac{121}{320}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{143}{320}\right)$	$e\left(\frac{317}{320}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{309}{320}\right)$	$e\left(\frac{311}{320}\right)$	$e\left(\frac{69}{160}\right)$	$e\left(\frac{43}{320}\right)$
$\chi_{6400}(21,\cdot)$	6400.dx	320	yes	$1$	$1$	$e\left(\frac{259}{320}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{117}{320}\right)$	$e\left(\frac{143}{320}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{311}{320}\right)$	$e\left(\frac{269}{320}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{137}{320}\right)$
$\chi_{6400}(23,\cdot)$	6400.dq	160	no	$1$	$1$	$e\left(\frac{1}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{117}{160}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{69}{160}\right)$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{3}{160}\right)$
$\chi_{6400}(27,\cdot)$	6400.dz	320	yes	$1$	$1$	$e\left(\frac{87}{320}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{87}{160}\right)$	$e\left(\frac{241}{320}\right)$	$e\left(\frac{19}{320}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{43}{320}\right)$	$e\left(\frac{137}{320}\right)$	$e\left(\frac{3}{160}\right)$	$e\left(\frac{261}{320}\right)$
$\chi_{6400}(29,\cdot)$	6400.du	320	yes	$1$	$1$	$e\left(\frac{309}{320}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{149}{160}\right)$	$e\left(\frac{307}{320}\right)$	$e\left(\frac{73}{320}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{320}\right)$	$e\left(\frac{219}{320}\right)$	$e\left(\frac{1}{160}\right)$	$e\left(\frac{287}{320}\right)$
$\chi_{6400}(31,\cdot)$	6400.cr	40	no	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$-i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{6400}(33,\cdot)$	6400.cm	40	no	$-1$	$1$	$e\left(\frac{27}{40}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{6400}(37,\cdot)$	6400.dt	320	yes	$-1$	$1$	$e\left(\frac{263}{320}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{129}{320}\right)$	$e\left(\frac{291}{320}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{27}{320}\right)$	$e\left(\frac{313}{320}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{149}{320}\right)$
$\chi_{6400}(39,\cdot)$	6400.do	160	no	$-1$	$1$	$e\left(\frac{71}{160}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{53}{160}\right)$
$\chi_{6400}(41,\cdot)$	6400.dp	160	no	$1$	$1$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{87}{160}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{147}{160}\right)$
$\chi_{6400}(43,\cdot)$	6400.da	64	no	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{64}\right)$
$\chi_{6400}(47,\cdot)$	6400.di	80	no	$1$	$1$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{6400}(49,\cdot)$	6400.bn	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{6400}(51,\cdot)$	6400.cz	64	no	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{55}{64}\right)$
$\chi_{6400}(53,\cdot)$	6400.dy	320	yes	$-1$	$1$	$e\left(\frac{59}{320}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{77}{320}\right)$	$e\left(\frac{103}{320}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{31}{320}\right)$	$e\left(\frac{229}{320}\right)$	$e\left(\frac{151}{160}\right)$	$e\left(\frac{177}{320}\right)$
$\chi_{6400}(57,\cdot)$	6400.ce	32	no	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{6400}(59,\cdot)$	6400.dw	320	yes	$-1$	$1$	$e\left(\frac{223}{320}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{63}{160}\right)$	$e\left(\frac{89}{320}\right)$	$e\left(\frac{251}{320}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{67}{320}\right)$	$e\left(\frac{113}{320}\right)$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{29}{320}\right)$
$\chi_{6400}(61,\cdot)$	6400.dx	320	yes	$1$	$1$	$e\left(\frac{317}{320}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{157}{160}\right)$	$e\left(\frac{11}{320}\right)$	$e\left(\frac{49}{320}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{73}{320}\right)$	$e\left(\frac{307}{320}\right)$	$e\left(\frac{153}{160}\right)$	$e\left(\frac{311}{320}\right)$
$\chi_{6400}(63,\cdot)$	6400.cc	20	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{6400}(67,\cdot)$	6400.ds	320	yes	$1$	$1$	$e\left(\frac{301}{320}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{203}{320}\right)$	$e\left(\frac{257}{320}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{169}{320}\right)$	$e\left(\frac{211}{320}\right)$	$e\left(\frac{129}{160}\right)$	$e\left(\frac{263}{320}\right)$
$\chi_{6400}(69,\cdot)$	6400.du	320	yes	$1$	$1$	$e\left(\frac{31}{320}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{153}{320}\right)$	$e\left(\frac{27}{320}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{259}{320}\right)$	$e\left(\frac{81}{320}\right)$	$e\left(\frac{99}{160}\right)$	$e\left(\frac{93}{320}\right)$
$\chi_{6400}(71,\cdot)$	6400.dm	160	no	$-1$	$1$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{101}{160}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{121}{160}\right)$
$\chi_{6400}(73,\cdot)$	6400.dr	160	no	$-1$	$1$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{83}{160}\right)$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{91}{160}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{23}{160}\right)$
$\chi_{6400}(77,\cdot)$	6400.dy	320	yes	$-1$	$1$	$e\left(\frac{97}{320}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{311}{320}\right)$	$e\left(\frac{229}{320}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{13}{320}\right)$	$e\left(\frac{127}{320}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{291}{320}\right)$
$\chi_{6400}(79,\cdot)$	6400.de	80	no	$-1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{73}{80}\right)$

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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	$6400$
Structure	\(C_{2}\times C_{4}\times C_{320}\)
Order	$2560$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{6400}(1,\cdot)\)	6400.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6400}(3,\cdot)\)	6400.dz	320	yes	\(1\)	\(1\)	\(e\left(\frac{29}{320}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{187}{320}\right)\)	\(e\left(\frac{113}{320}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{121}{320}\right)\)	\(e\left(\frac{259}{320}\right)\)	\(e\left(\frac{1}{160}\right)\)	\(e\left(\frac{87}{320}\right)\)
\(\chi_{6400}(7,\cdot)\)	6400.cf	32	no	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{6400}(9,\cdot)\)	6400.dn	160	no	\(1\)	\(1\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{87}{160}\right)\)
\(\chi_{6400}(11,\cdot)\)	6400.dv	320	yes	\(-1\)	\(1\)	\(e\left(\frac{187}{320}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{61}{320}\right)\)	\(e\left(\frac{199}{320}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{143}{320}\right)\)	\(e\left(\frac{117}{320}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{241}{320}\right)\)
\(\chi_{6400}(13,\cdot)\)	6400.dt	320	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{320}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{199}{320}\right)\)	\(e\left(\frac{181}{320}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{317}{320}\right)\)	\(e\left(\frac{143}{320}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{19}{320}\right)\)
\(\chi_{6400}(17,\cdot)\)	6400.dj	80	no	\(-1\)	\(1\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{6400}(19,\cdot)\)	6400.dw	320	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{320}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{143}{320}\right)\)	\(e\left(\frac{317}{320}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{309}{320}\right)\)	\(e\left(\frac{311}{320}\right)\)	\(e\left(\frac{69}{160}\right)\)	\(e\left(\frac{43}{320}\right)\)
\(\chi_{6400}(21,\cdot)\)	6400.dx	320	yes	\(1\)	\(1\)	\(e\left(\frac{259}{320}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{117}{320}\right)\)	\(e\left(\frac{143}{320}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{311}{320}\right)\)	\(e\left(\frac{269}{320}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{137}{320}\right)\)
\(\chi_{6400}(23,\cdot)\)	6400.dq	160	no	\(1\)	\(1\)	\(e\left(\frac{1}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{117}{160}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{69}{160}\right)\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{3}{160}\right)\)
\(\chi_{6400}(27,\cdot)\)	6400.dz	320	yes	\(1\)	\(1\)	\(e\left(\frac{87}{320}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{87}{160}\right)\)	\(e\left(\frac{241}{320}\right)\)	\(e\left(\frac{19}{320}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{43}{320}\right)\)	\(e\left(\frac{137}{320}\right)\)	\(e\left(\frac{3}{160}\right)\)	\(e\left(\frac{261}{320}\right)\)
\(\chi_{6400}(29,\cdot)\)	6400.du	320	yes	\(1\)	\(1\)	\(e\left(\frac{309}{320}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{149}{160}\right)\)	\(e\left(\frac{307}{320}\right)\)	\(e\left(\frac{73}{320}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{320}\right)\)	\(e\left(\frac{219}{320}\right)\)	\(e\left(\frac{1}{160}\right)\)	\(e\left(\frac{287}{320}\right)\)
\(\chi_{6400}(31,\cdot)\)	6400.cr	40	no	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(-i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{6400}(33,\cdot)\)	6400.cm	40	no	\(-1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{6400}(37,\cdot)\)	6400.dt	320	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{320}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{129}{320}\right)\)	\(e\left(\frac{291}{320}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{27}{320}\right)\)	\(e\left(\frac{313}{320}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{149}{320}\right)\)
\(\chi_{6400}(39,\cdot)\)	6400.do	160	no	\(-1\)	\(1\)	\(e\left(\frac{71}{160}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{53}{160}\right)\)
\(\chi_{6400}(41,\cdot)\)	6400.dp	160	no	\(1\)	\(1\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{87}{160}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{147}{160}\right)\)
\(\chi_{6400}(43,\cdot)\)	6400.da	64	no	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)
\(\chi_{6400}(47,\cdot)\)	6400.di	80	no	\(1\)	\(1\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{6400}(49,\cdot)\)	6400.bn	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{6400}(51,\cdot)\)	6400.cz	64	no	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)
\(\chi_{6400}(53,\cdot)\)	6400.dy	320	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{320}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{77}{320}\right)\)	\(e\left(\frac{103}{320}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{31}{320}\right)\)	\(e\left(\frac{229}{320}\right)\)	\(e\left(\frac{151}{160}\right)\)	\(e\left(\frac{177}{320}\right)\)
\(\chi_{6400}(57,\cdot)\)	6400.ce	32	no	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{6400}(59,\cdot)\)	6400.dw	320	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{320}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{63}{160}\right)\)	\(e\left(\frac{89}{320}\right)\)	\(e\left(\frac{251}{320}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{67}{320}\right)\)	\(e\left(\frac{113}{320}\right)\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{29}{320}\right)\)
\(\chi_{6400}(61,\cdot)\)	6400.dx	320	yes	\(1\)	\(1\)	\(e\left(\frac{317}{320}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{157}{160}\right)\)	\(e\left(\frac{11}{320}\right)\)	\(e\left(\frac{49}{320}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{73}{320}\right)\)	\(e\left(\frac{307}{320}\right)\)	\(e\left(\frac{153}{160}\right)\)	\(e\left(\frac{311}{320}\right)\)
\(\chi_{6400}(63,\cdot)\)	6400.cc	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{6400}(67,\cdot)\)	6400.ds	320	yes	\(1\)	\(1\)	\(e\left(\frac{301}{320}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{203}{320}\right)\)	\(e\left(\frac{257}{320}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{169}{320}\right)\)	\(e\left(\frac{211}{320}\right)\)	\(e\left(\frac{129}{160}\right)\)	\(e\left(\frac{263}{320}\right)\)
\(\chi_{6400}(69,\cdot)\)	6400.du	320	yes	\(1\)	\(1\)	\(e\left(\frac{31}{320}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{153}{320}\right)\)	\(e\left(\frac{27}{320}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{259}{320}\right)\)	\(e\left(\frac{81}{320}\right)\)	\(e\left(\frac{99}{160}\right)\)	\(e\left(\frac{93}{320}\right)\)
\(\chi_{6400}(71,\cdot)\)	6400.dm	160	no	\(-1\)	\(1\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{101}{160}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{121}{160}\right)\)
\(\chi_{6400}(73,\cdot)\)	6400.dr	160	no	\(-1\)	\(1\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{83}{160}\right)\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{91}{160}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{23}{160}\right)\)
\(\chi_{6400}(77,\cdot)\)	6400.dy	320	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{320}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{311}{320}\right)\)	\(e\left(\frac{229}{320}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{13}{320}\right)\)	\(e\left(\frac{127}{320}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{291}{320}\right)\)
\(\chi_{6400}(79,\cdot)\)	6400.de	80	no	\(-1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)

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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.