LMFDB - Group of Dirichlet characters of modulus 16335

Show commands: PariGP / SageMath

sage: H = DirichletGroup(16335)

pari: g = idealstar(,16335,2)

Character group

sage: G.order() pari: g.no
Order	=	7920
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1980}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{16335}(3026,\cdot)$, $\chi_{16335}(9802,\cdot)$, $\chi_{16335}(3511,\cdot)$

First 32 of 7920 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$19$	$23$
$\chi_{16335}(1,\cdot)$	16335.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{16335}(2,\cdot)$	16335.fk	1980	yes	$-1$	$1$	$e\left(\frac{623}{1980}\right)$	$e\left(\frac{623}{990}\right)$	$e\left(\frac{401}{1980}\right)$	$e\left(\frac{623}{660}\right)$	$e\left(\frac{223}{1980}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{349}{660}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{395}{396}\right)$
$\chi_{16335}(4,\cdot)$	16335.fh	990	yes	$1$	$1$	$e\left(\frac{623}{990}\right)$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{401}{990}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{223}{990}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{197}{198}\right)$
$\chi_{16335}(7,\cdot)$	16335.fl	1980	yes	$1$	$1$	$e\left(\frac{401}{1980}\right)$	$e\left(\frac{401}{990}\right)$	$e\left(\frac{1817}{1980}\right)$	$e\left(\frac{401}{660}\right)$	$e\left(\frac{571}{1980}\right)$	$e\left(\frac{119}{990}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{463}{660}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{389}{396}\right)$
$\chi_{16335}(8,\cdot)$	16335.fa	660	no	$-1$	$1$	$e\left(\frac{623}{660}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{401}{660}\right)$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{223}{660}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{131}{132}\right)$
$\chi_{16335}(13,\cdot)$	16335.fl	1980	yes	$1$	$1$	$e\left(\frac{223}{1980}\right)$	$e\left(\frac{223}{990}\right)$	$e\left(\frac{571}{1980}\right)$	$e\left(\frac{223}{660}\right)$	$e\left(\frac{1073}{1980}\right)$	$e\left(\frac{397}{990}\right)$	$e\left(\frac{223}{495}\right)$	$e\left(\frac{269}{660}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{163}{396}\right)$
$\chi_{16335}(14,\cdot)$	16335.fd	990	yes	$-1$	$1$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{119}{990}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{397}{990}\right)$	$e\left(\frac{631}{990}\right)$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{97}{99}\right)$
$\chi_{16335}(16,\cdot)$	16335.ey	495	no	$1$	$1$	$e\left(\frac{128}{495}\right)$	$e\left(\frac{256}{495}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{223}{495}\right)$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{17}{495}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{98}{99}\right)$
$\chi_{16335}(17,\cdot)$	16335.fa	660	no	$-1$	$1$	$e\left(\frac{349}{660}\right)$	$e\left(\frac{19}{330}\right)$	$e\left(\frac{463}{660}\right)$	$e\left(\frac{129}{220}\right)$	$e\left(\frac{269}{660}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{13}{132}\right)$
$\chi_{16335}(19,\cdot)$	16335.en	330	no	$-1$	$1$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{16335}(23,\cdot)$	16335.ev	396	yes	$1$	$1$	$e\left(\frac{395}{396}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{163}{396}\right)$	$e\left(\frac{97}{99}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{205}{396}\right)$
$\chi_{16335}(26,\cdot)$	16335.dp	110	no	$-1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{16335}(28,\cdot)$	16335.ek	220	no	$1$	$1$	$e\left(\frac{183}{220}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{71}{220}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{113}{220}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{167}{220}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{16335}(29,\cdot)$	16335.fi	990	yes	$1$	$1$	$e\left(\frac{703}{990}\right)$	$e\left(\frac{208}{495}\right)$	$e\left(\frac{233}{495}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{274}{495}\right)$	$e\left(\frac{179}{990}\right)$	$e\left(\frac{416}{495}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{92}{99}\right)$
$\chi_{16335}(31,\cdot)$	16335.ey	495	no	$1$	$1$	$e\left(\frac{442}{495}\right)$	$e\left(\frac{389}{495}\right)$	$e\left(\frac{124}{495}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{422}{495}\right)$	$e\left(\frac{71}{495}\right)$	$e\left(\frac{283}{495}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{94}{99}\right)$
$\chi_{16335}(32,\cdot)$	16335.ex	396	yes	$-1$	$1$	$e\left(\frac{227}{396}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{5}{396}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{223}{396}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{391}{396}\right)$
$\chi_{16335}(34,\cdot)$	16335.ee	198	yes	$1$	$1$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{179}{198}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{103}{198}\right)$	$e\left(\frac{74}{99}\right)$	$e\left(\frac{37}{99}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{19}{198}\right)$
$\chi_{16335}(37,\cdot)$	16335.fb	660	no	$-1$	$1$	$e\left(\frac{637}{660}\right)$	$e\left(\frac{307}{330}\right)$	$e\left(\frac{169}{660}\right)$	$e\left(\frac{197}{220}\right)$	$e\left(\frac{647}{660}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{211}{220}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{19}{132}\right)$
$\chi_{16335}(38,\cdot)$	16335.fm	1980	yes	$1$	$1$	$e\left(\frac{467}{1980}\right)$	$e\left(\frac{467}{990}\right)$	$e\left(\frac{1289}{1980}\right)$	$e\left(\frac{467}{660}\right)$	$e\left(\frac{307}{1980}\right)$	$e\left(\frac{439}{495}\right)$	$e\left(\frac{467}{495}\right)$	$e\left(\frac{1}{660}\right)$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{257}{396}\right)$
$\chi_{16335}(41,\cdot)$	16335.fe	990	no	$1$	$1$	$e\left(\frac{76}{495}\right)$	$e\left(\frac{152}{495}\right)$	$e\left(\frac{569}{990}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{667}{990}\right)$	$e\left(\frac{721}{990}\right)$	$e\left(\frac{304}{495}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{5}{198}\right)$
$\chi_{16335}(43,\cdot)$	16335.ew	396	yes	$1$	$1$	$e\left(\frac{79}{396}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{355}{396}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{19}{198}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{239}{396}\right)$
$\chi_{16335}(46,\cdot)$	16335.es	330	no	$-1$	$1$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{173}{330}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{16335}(47,\cdot)$	16335.fm	1980	yes	$1$	$1$	$e\left(\frac{1049}{1980}\right)$	$e\left(\frac{59}{990}\right)$	$e\left(\frac{1403}{1980}\right)$	$e\left(\frac{389}{660}\right)$	$e\left(\frac{1669}{1980}\right)$	$e\left(\frac{118}{495}\right)$	$e\left(\frac{59}{495}\right)$	$e\left(\frac{487}{660}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{155}{396}\right)$
$\chi_{16335}(49,\cdot)$	16335.fh	990	yes	$1$	$1$	$e\left(\frac{401}{990}\right)$	$e\left(\frac{401}{495}\right)$	$e\left(\frac{827}{990}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{571}{990}\right)$	$e\left(\frac{119}{495}\right)$	$e\left(\frac{307}{495}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{191}{198}\right)$
$\chi_{16335}(52,\cdot)$	16335.fl	1980	yes	$1$	$1$	$e\left(\frac{1469}{1980}\right)$	$e\left(\frac{479}{990}\right)$	$e\left(\frac{1373}{1980}\right)$	$e\left(\frac{149}{660}\right)$	$e\left(\frac{1519}{1980}\right)$	$e\left(\frac{431}{990}\right)$	$e\left(\frac{479}{495}\right)$	$e\left(\frac{307}{660}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{161}{396}\right)$
$\chi_{16335}(53,\cdot)$	16335.el	220	no	$1$	$1$	$e\left(\frac{47}{220}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{109}{220}\right)$	$e\left(\frac{141}{220}\right)$	$e\left(\frac{127}{220}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{103}{220}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{16335}(56,\cdot)$	16335.ef	198	no	$-1$	$1$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{62}{99}\right)$	$e\left(\frac{133}{198}\right)$	$e\left(\frac{58}{99}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{193}{198}\right)$
$\chi_{16335}(58,\cdot)$	16335.fn	1980	yes	$-1$	$1$	$e\left(\frac{49}{1980}\right)$	$e\left(\frac{49}{990}\right)$	$e\left(\frac{1333}{1980}\right)$	$e\left(\frac{49}{660}\right)$	$e\left(\frac{1319}{1980}\right)$	$e\left(\frac{691}{990}\right)$	$e\left(\frac{49}{495}\right)$	$e\left(\frac{287}{660}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{367}{396}\right)$
$\chi_{16335}(59,\cdot)$	16335.fd	990	yes	$-1$	$1$	$e\left(\frac{34}{495}\right)$	$e\left(\frac{68}{495}\right)$	$e\left(\frac{971}{990}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{103}{990}\right)$	$e\left(\frac{49}{990}\right)$	$e\left(\frac{136}{495}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{91}{99}\right)$
$\chi_{16335}(61,\cdot)$	16335.fj	990	no	$-1$	$1$	$e\left(\frac{871}{990}\right)$	$e\left(\frac{376}{495}\right)$	$e\left(\frac{157}{990}\right)$	$e\left(\frac{211}{330}\right)$	$e\left(\frac{191}{990}\right)$	$e\left(\frac{19}{495}\right)$	$e\left(\frac{257}{495}\right)$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{301}{330}\right)$	$e\left(\frac{14}{99}\right)$
$\chi_{16335}(62,\cdot)$	16335.fa	660	no	$-1$	$1$	$e\left(\frac{137}{660}\right)$	$e\left(\frac{137}{330}\right)$	$e\left(\frac{299}{660}\right)$	$e\left(\frac{137}{220}\right)$	$e\left(\frac{637}{660}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{111}{220}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{125}{132}\right)$
$\chi_{16335}(64,\cdot)$	16335.et	330	no	$1$	$1$	$e\left(\frac{293}{330}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{223}{330}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{65}{66}\right)$

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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	$16335$
Structure	\(C_{2}\times C_{2}\times C_{1980}\)
Order	$7920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)	\(23\)
\(\chi_{16335}(1,\cdot)\)	16335.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{16335}(2,\cdot)\)	16335.fk	1980	yes	\(-1\)	\(1\)	\(e\left(\frac{623}{1980}\right)\)	\(e\left(\frac{623}{990}\right)\)	\(e\left(\frac{401}{1980}\right)\)	\(e\left(\frac{623}{660}\right)\)	\(e\left(\frac{223}{1980}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{349}{660}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{395}{396}\right)\)
\(\chi_{16335}(4,\cdot)\)	16335.fh	990	yes	\(1\)	\(1\)	\(e\left(\frac{623}{990}\right)\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{401}{990}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{223}{990}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{197}{198}\right)\)
\(\chi_{16335}(7,\cdot)\)	16335.fl	1980	yes	\(1\)	\(1\)	\(e\left(\frac{401}{1980}\right)\)	\(e\left(\frac{401}{990}\right)\)	\(e\left(\frac{1817}{1980}\right)\)	\(e\left(\frac{401}{660}\right)\)	\(e\left(\frac{571}{1980}\right)\)	\(e\left(\frac{119}{990}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{463}{660}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{389}{396}\right)\)
\(\chi_{16335}(8,\cdot)\)	16335.fa	660	no	\(-1\)	\(1\)	\(e\left(\frac{623}{660}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{401}{660}\right)\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{223}{660}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{131}{132}\right)\)
\(\chi_{16335}(13,\cdot)\)	16335.fl	1980	yes	\(1\)	\(1\)	\(e\left(\frac{223}{1980}\right)\)	\(e\left(\frac{223}{990}\right)\)	\(e\left(\frac{571}{1980}\right)\)	\(e\left(\frac{223}{660}\right)\)	\(e\left(\frac{1073}{1980}\right)\)	\(e\left(\frac{397}{990}\right)\)	\(e\left(\frac{223}{495}\right)\)	\(e\left(\frac{269}{660}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{163}{396}\right)\)
\(\chi_{16335}(14,\cdot)\)	16335.fd	990	yes	\(-1\)	\(1\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{119}{990}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{397}{990}\right)\)	\(e\left(\frac{631}{990}\right)\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{97}{99}\right)\)
\(\chi_{16335}(16,\cdot)\)	16335.ey	495	no	\(1\)	\(1\)	\(e\left(\frac{128}{495}\right)\)	\(e\left(\frac{256}{495}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{223}{495}\right)\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{17}{495}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{98}{99}\right)\)
\(\chi_{16335}(17,\cdot)\)	16335.fa	660	no	\(-1\)	\(1\)	\(e\left(\frac{349}{660}\right)\)	\(e\left(\frac{19}{330}\right)\)	\(e\left(\frac{463}{660}\right)\)	\(e\left(\frac{129}{220}\right)\)	\(e\left(\frac{269}{660}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{13}{132}\right)\)
\(\chi_{16335}(19,\cdot)\)	16335.en	330	no	\(-1\)	\(1\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{16335}(23,\cdot)\)	16335.ev	396	yes	\(1\)	\(1\)	\(e\left(\frac{395}{396}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{163}{396}\right)\)	\(e\left(\frac{97}{99}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{205}{396}\right)\)
\(\chi_{16335}(26,\cdot)\)	16335.dp	110	no	\(-1\)	\(1\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{16335}(28,\cdot)\)	16335.ek	220	no	\(1\)	\(1\)	\(e\left(\frac{183}{220}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{71}{220}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{113}{220}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{167}{220}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{16335}(29,\cdot)\)	16335.fi	990	yes	\(1\)	\(1\)	\(e\left(\frac{703}{990}\right)\)	\(e\left(\frac{208}{495}\right)\)	\(e\left(\frac{233}{495}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{274}{495}\right)\)	\(e\left(\frac{179}{990}\right)\)	\(e\left(\frac{416}{495}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{92}{99}\right)\)
\(\chi_{16335}(31,\cdot)\)	16335.ey	495	no	\(1\)	\(1\)	\(e\left(\frac{442}{495}\right)\)	\(e\left(\frac{389}{495}\right)\)	\(e\left(\frac{124}{495}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{422}{495}\right)\)	\(e\left(\frac{71}{495}\right)\)	\(e\left(\frac{283}{495}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{94}{99}\right)\)
\(\chi_{16335}(32,\cdot)\)	16335.ex	396	yes	\(-1\)	\(1\)	\(e\left(\frac{227}{396}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{5}{396}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{223}{396}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{391}{396}\right)\)
\(\chi_{16335}(34,\cdot)\)	16335.ee	198	yes	\(1\)	\(1\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{179}{198}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{103}{198}\right)\)	\(e\left(\frac{74}{99}\right)\)	\(e\left(\frac{37}{99}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{19}{198}\right)\)
\(\chi_{16335}(37,\cdot)\)	16335.fb	660	no	\(-1\)	\(1\)	\(e\left(\frac{637}{660}\right)\)	\(e\left(\frac{307}{330}\right)\)	\(e\left(\frac{169}{660}\right)\)	\(e\left(\frac{197}{220}\right)\)	\(e\left(\frac{647}{660}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{211}{220}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{19}{132}\right)\)
\(\chi_{16335}(38,\cdot)\)	16335.fm	1980	yes	\(1\)	\(1\)	\(e\left(\frac{467}{1980}\right)\)	\(e\left(\frac{467}{990}\right)\)	\(e\left(\frac{1289}{1980}\right)\)	\(e\left(\frac{467}{660}\right)\)	\(e\left(\frac{307}{1980}\right)\)	\(e\left(\frac{439}{495}\right)\)	\(e\left(\frac{467}{495}\right)\)	\(e\left(\frac{1}{660}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{257}{396}\right)\)
\(\chi_{16335}(41,\cdot)\)	16335.fe	990	no	\(1\)	\(1\)	\(e\left(\frac{76}{495}\right)\)	\(e\left(\frac{152}{495}\right)\)	\(e\left(\frac{569}{990}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{667}{990}\right)\)	\(e\left(\frac{721}{990}\right)\)	\(e\left(\frac{304}{495}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{5}{198}\right)\)
\(\chi_{16335}(43,\cdot)\)	16335.ew	396	yes	\(1\)	\(1\)	\(e\left(\frac{79}{396}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{355}{396}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{19}{198}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{239}{396}\right)\)
\(\chi_{16335}(46,\cdot)\)	16335.es	330	no	\(-1\)	\(1\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{173}{330}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{16335}(47,\cdot)\)	16335.fm	1980	yes	\(1\)	\(1\)	\(e\left(\frac{1049}{1980}\right)\)	\(e\left(\frac{59}{990}\right)\)	\(e\left(\frac{1403}{1980}\right)\)	\(e\left(\frac{389}{660}\right)\)	\(e\left(\frac{1669}{1980}\right)\)	\(e\left(\frac{118}{495}\right)\)	\(e\left(\frac{59}{495}\right)\)	\(e\left(\frac{487}{660}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{155}{396}\right)\)
\(\chi_{16335}(49,\cdot)\)	16335.fh	990	yes	\(1\)	\(1\)	\(e\left(\frac{401}{990}\right)\)	\(e\left(\frac{401}{495}\right)\)	\(e\left(\frac{827}{990}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{571}{990}\right)\)	\(e\left(\frac{119}{495}\right)\)	\(e\left(\frac{307}{495}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{191}{198}\right)\)
\(\chi_{16335}(52,\cdot)\)	16335.fl	1980	yes	\(1\)	\(1\)	\(e\left(\frac{1469}{1980}\right)\)	\(e\left(\frac{479}{990}\right)\)	\(e\left(\frac{1373}{1980}\right)\)	\(e\left(\frac{149}{660}\right)\)	\(e\left(\frac{1519}{1980}\right)\)	\(e\left(\frac{431}{990}\right)\)	\(e\left(\frac{479}{495}\right)\)	\(e\left(\frac{307}{660}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{161}{396}\right)\)
\(\chi_{16335}(53,\cdot)\)	16335.el	220	no	\(1\)	\(1\)	\(e\left(\frac{47}{220}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{109}{220}\right)\)	\(e\left(\frac{141}{220}\right)\)	\(e\left(\frac{127}{220}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{103}{220}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{16335}(56,\cdot)\)	16335.ef	198	no	\(-1\)	\(1\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{62}{99}\right)\)	\(e\left(\frac{133}{198}\right)\)	\(e\left(\frac{58}{99}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{193}{198}\right)\)
\(\chi_{16335}(58,\cdot)\)	16335.fn	1980	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{1980}\right)\)	\(e\left(\frac{49}{990}\right)\)	\(e\left(\frac{1333}{1980}\right)\)	\(e\left(\frac{49}{660}\right)\)	\(e\left(\frac{1319}{1980}\right)\)	\(e\left(\frac{691}{990}\right)\)	\(e\left(\frac{49}{495}\right)\)	\(e\left(\frac{287}{660}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{367}{396}\right)\)
\(\chi_{16335}(59,\cdot)\)	16335.fd	990	yes	\(-1\)	\(1\)	\(e\left(\frac{34}{495}\right)\)	\(e\left(\frac{68}{495}\right)\)	\(e\left(\frac{971}{990}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{103}{990}\right)\)	\(e\left(\frac{49}{990}\right)\)	\(e\left(\frac{136}{495}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{91}{99}\right)\)
\(\chi_{16335}(61,\cdot)\)	16335.fj	990	no	\(-1\)	\(1\)	\(e\left(\frac{871}{990}\right)\)	\(e\left(\frac{376}{495}\right)\)	\(e\left(\frac{157}{990}\right)\)	\(e\left(\frac{211}{330}\right)\)	\(e\left(\frac{191}{990}\right)\)	\(e\left(\frac{19}{495}\right)\)	\(e\left(\frac{257}{495}\right)\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{301}{330}\right)\)	\(e\left(\frac{14}{99}\right)\)
\(\chi_{16335}(62,\cdot)\)	16335.fa	660	no	\(-1\)	\(1\)	\(e\left(\frac{137}{660}\right)\)	\(e\left(\frac{137}{330}\right)\)	\(e\left(\frac{299}{660}\right)\)	\(e\left(\frac{137}{220}\right)\)	\(e\left(\frac{637}{660}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{111}{220}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{125}{132}\right)\)
\(\chi_{16335}(64,\cdot)\)	16335.et	330	no	\(1\)	\(1\)	\(e\left(\frac{293}{330}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{223}{330}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{65}{66}\right)\)

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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.