LMFDB - Group of Dirichlet characters of modulus 100016

Show commands: PariGP / SageMath

sage: H = DirichletGroup(100016)

pari: g = idealstar(,100016,2)

Character group

sage: G.order() pari: g.no
Order	=	39744
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{828}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{100016}(62511,\cdot)$, $\chi_{100016}(75013,\cdot)$, $\chi_{100016}(28577,\cdot)$, $\chi_{100016}(5265,\cdot)$, $\chi_{100016}(46817,\cdot)$

First 32 of 39744 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{100016}(1,\cdot)$	100016.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{100016}(3,\cdot)$	100016.bdm	828	yes	$-1$	$1$	$e\left(\frac{1}{828}\right)$	$e\left(\frac{475}{828}\right)$	$e\left(\frac{1}{414}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{119}{828}\right)$	$e\left(\frac{119}{207}\right)$	$e\left(\frac{143}{414}\right)$	$e\left(\frac{197}{207}\right)$	$e\left(\frac{61}{414}\right)$	$e\left(\frac{1}{276}\right)$
$\chi_{100016}(5,\cdot)$	100016.bdb	828	yes	$1$	$1$	$e\left(\frac{475}{828}\right)$	$e\left(\frac{547}{828}\right)$	$e\left(\frac{61}{414}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{773}{828}\right)$	$e\left(\frac{97}{414}\right)$	$e\left(\frac{29}{414}\right)$	$e\left(\frac{11}{207}\right)$	$e\left(\frac{133}{414}\right)$	$e\left(\frac{199}{276}\right)$
$\chi_{100016}(9,\cdot)$	100016.yt	414	no	$1$	$1$	$e\left(\frac{1}{414}\right)$	$e\left(\frac{61}{414}\right)$	$e\left(\frac{1}{207}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{119}{414}\right)$	$e\left(\frac{31}{207}\right)$	$e\left(\frac{143}{207}\right)$	$e\left(\frac{187}{207}\right)$	$e\left(\frac{61}{207}\right)$	$e\left(\frac{1}{138}\right)$
$\chi_{100016}(11,\cdot)$	100016.xa	276	yes	$1$	$1$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{133}{276}\right)$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{81}{92}\right)$
$\chi_{100016}(13,\cdot)$	100016.bca	828	yes	$-1$	$1$	$e\left(\frac{119}{828}\right)$	$e\left(\frac{773}{828}\right)$	$e\left(\frac{119}{414}\right)$	$e\left(\frac{209}{276}\right)$	$e\left(\frac{637}{828}\right)$	$e\left(\frac{16}{207}\right)$	$e\left(\frac{43}{414}\right)$	$e\left(\frac{52}{207}\right)$	$e\left(\frac{359}{414}\right)$	$e\left(\frac{119}{276}\right)$
$\chi_{100016}(15,\cdot)$	100016.bat	414	no	$-1$	$1$	$e\left(\frac{119}{207}\right)$	$e\left(\frac{97}{414}\right)$	$e\left(\frac{31}{207}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{16}{207}\right)$	$e\left(\frac{335}{414}\right)$	$e\left(\frac{86}{207}\right)$	$e\left(\frac{1}{207}\right)$	$e\left(\frac{97}{207}\right)$	$e\left(\frac{50}{69}\right)$
$\chi_{100016}(17,\cdot)$	100016.ban	414	no	$-1$	$1$	$e\left(\frac{143}{414}\right)$	$e\left(\frac{29}{414}\right)$	$e\left(\frac{143}{207}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{43}{414}\right)$	$e\left(\frac{86}{207}\right)$	$e\left(\frac{119}{414}\right)$	$e\left(\frac{38}{207}\right)$	$e\left(\frac{29}{207}\right)$	$e\left(\frac{5}{138}\right)$
$\chi_{100016}(23,\cdot)$	100016.zj	414	no	$1$	$1$	$e\left(\frac{197}{207}\right)$	$e\left(\frac{11}{207}\right)$	$e\left(\frac{187}{207}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{52}{207}\right)$	$e\left(\frac{1}{207}\right)$	$e\left(\frac{38}{207}\right)$	$e\left(\frac{193}{207}\right)$	$e\left(\frac{22}{207}\right)$	$e\left(\frac{59}{69}\right)$
$\chi_{100016}(25,\cdot)$	100016.bbh	414	no	$1$	$1$	$e\left(\frac{61}{414}\right)$	$e\left(\frac{133}{414}\right)$	$e\left(\frac{61}{207}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{359}{414}\right)$	$e\left(\frac{97}{207}\right)$	$e\left(\frac{29}{207}\right)$	$e\left(\frac{22}{207}\right)$	$e\left(\frac{133}{207}\right)$	$e\left(\frac{61}{138}\right)$
$\chi_{100016}(27,\cdot)$	100016.wu	276	yes	$-1$	$1$	$e\left(\frac{1}{276}\right)$	$e\left(\frac{199}{276}\right)$	$e\left(\frac{1}{138}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{119}{276}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{61}{138}\right)$	$e\left(\frac{1}{92}\right)$
$\chi_{100016}(29,\cdot)$	100016.bcr	828	no	$1$	$1$	$e\left(\frac{617}{828}\right)$	$e\left(\frac{515}{828}\right)$	$e\left(\frac{203}{414}\right)$	$e\left(\frac{113}{276}\right)$	$e\left(\frac{283}{828}\right)$	$e\left(\frac{76}{207}\right)$	$e\left(\frac{128}{207}\right)$	$e\left(\frac{40}{207}\right)$	$e\left(\frac{101}{414}\right)$	$e\left(\frac{65}{276}\right)$
$\chi_{100016}(31,\cdot)$	100016.vl	138	no	$1$	$1$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{43}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{5}{138}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{19}{46}\right)$
$\chi_{100016}(33,\cdot)$	100016.bbk	414	no	$-1$	$1$	$e\left(\frac{130}{207}\right)$	$e\left(\frac{202}{207}\right)$	$e\left(\frac{53}{207}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{373}{414}\right)$	$e\left(\frac{125}{207}\right)$	$e\left(\frac{47}{414}\right)$	$e\left(\frac{157}{414}\right)$	$e\left(\frac{197}{207}\right)$	$e\left(\frac{61}{69}\right)$
$\chi_{100016}(37,\cdot)$	100016.xj	276	yes	$-1$	$1$	$e\left(\frac{233}{276}\right)$	$e\left(\frac{229}{276}\right)$	$e\left(\frac{95}{138}\right)$	$e\left(\frac{269}{276}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{65}{69}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{91}{138}\right)$	$e\left(\frac{49}{92}\right)$
$\chi_{100016}(39,\cdot)$	100016.ug	138	no	$1$	$1$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{14}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{10}{23}\right)$
$\chi_{100016}(41,\cdot)$	100016.bad	414	no	$-1$	$1$	$e\left(\frac{377}{414}\right)$	$e\left(\frac{365}{414}\right)$	$e\left(\frac{170}{207}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{41}{207}\right)$	$e\left(\frac{164}{207}\right)$	$e\left(\frac{389}{414}\right)$	$e\left(\frac{31}{414}\right)$	$e\left(\frac{158}{207}\right)$	$e\left(\frac{101}{138}\right)$
$\chi_{100016}(43,\cdot)$	100016.bdf	828	no	$1$	$1$	$e\left(\frac{379}{828}\right)$	$e\left(\frac{625}{828}\right)$	$e\left(\frac{379}{414}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{251}{828}\right)$	$e\left(\frac{44}{207}\right)$	$e\left(\frac{85}{207}\right)$	$e\left(\frac{79}{414}\right)$	$e\left(\frac{211}{414}\right)$	$e\left(\frac{103}{276}\right)$
$\chi_{100016}(45,\cdot)$	100016.xs	276	yes	$1$	$1$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{223}{276}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{181}{276}\right)$	$e\left(\frac{61}{276}\right)$	$e\left(\frac{53}{138}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{67}{92}\right)$
$\chi_{100016}(51,\cdot)$	100016.bbz	828	yes	$1$	$1$	$e\left(\frac{287}{828}\right)$	$e\left(\frac{533}{828}\right)$	$e\left(\frac{287}{414}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{205}{828}\right)$	$e\left(\frac{205}{207}\right)$	$e\left(\frac{131}{207}\right)$	$e\left(\frac{28}{207}\right)$	$e\left(\frac{119}{414}\right)$	$e\left(\frac{11}{276}\right)$
$\chi_{100016}(53,\cdot)$	100016.bcf	828	yes	$-1$	$1$	$e\left(\frac{731}{828}\right)$	$e\left(\frac{155}{828}\right)$	$e\left(\frac{317}{414}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{739}{828}\right)$	$e\left(\frac{29}{414}\right)$	$e\left(\frac{206}{207}\right)$	$e\left(\frac{77}{414}\right)$	$e\left(\frac{155}{414}\right)$	$e\left(\frac{179}{276}\right)$
$\chi_{100016}(55,\cdot)$	100016.baj	414	no	$1$	$1$	$e\left(\frac{83}{414}\right)$	$e\left(\frac{13}{207}\right)$	$e\left(\frac{83}{207}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{143}{207}\right)$	$e\left(\frac{109}{414}\right)$	$e\left(\frac{347}{414}\right)$	$e\left(\frac{199}{414}\right)$	$e\left(\frac{26}{207}\right)$	$e\left(\frac{83}{138}\right)$
$\chi_{100016}(59,\cdot)$	100016.bdm	828	yes	$-1$	$1$	$e\left(\frac{403}{828}\right)$	$e\left(\frac{157}{828}\right)$	$e\left(\frac{403}{414}\right)$	$e\left(\frac{167}{276}\right)$	$e\left(\frac{761}{828}\right)$	$e\left(\frac{140}{207}\right)$	$e\left(\frac{83}{414}\right)$	$e\left(\frac{110}{207}\right)$	$e\left(\frac{157}{414}\right)$	$e\left(\frac{127}{276}\right)$
$\chi_{100016}(61,\cdot)$	100016.bdg	828	yes	$-1$	$1$	$e\left(\frac{221}{828}\right)$	$e\left(\frac{647}{828}\right)$	$e\left(\frac{221}{414}\right)$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{217}{828}\right)$	$e\left(\frac{10}{207}\right)$	$e\left(\frac{139}{414}\right)$	$e\left(\frac{341}{414}\right)$	$e\left(\frac{233}{414}\right)$	$e\left(\frac{221}{276}\right)$
$\chi_{100016}(65,\cdot)$	100016.vk	138	no	$-1$	$1$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{7}{46}\right)$
$\chi_{100016}(67,\cdot)$	100016.bce	828	yes	$-1$	$1$	$e\left(\frac{647}{828}\right)$	$e\left(\frac{827}{828}\right)$	$e\left(\frac{233}{414}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{679}{828}\right)$	$e\left(\frac{323}{414}\right)$	$e\left(\frac{203}{207}\right)$	$e\left(\frac{101}{414}\right)$	$e\left(\frac{413}{414}\right)$	$e\left(\frac{95}{276}\right)$
$\chi_{100016}(69,\cdot)$	100016.wt	276	yes	$-1$	$1$	$e\left(\frac{263}{276}\right)$	$e\left(\frac{173}{276}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{109}{276}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{73}{138}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{35}{138}\right)$	$e\left(\frac{79}{92}\right)$
$\chi_{100016}(71,\cdot)$	100016.bah	414	no	$1$	$1$	$e\left(\frac{95}{414}\right)$	$e\left(\frac{137}{414}\right)$	$e\left(\frac{95}{207}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{29}{207}\right)$	$e\left(\frac{116}{207}\right)$	$e\left(\frac{130}{207}\right)$	$e\left(\frac{133}{414}\right)$	$e\left(\frac{137}{207}\right)$	$e\left(\frac{95}{138}\right)$
$\chi_{100016}(73,\cdot)$	100016.bao	414	no	$1$	$1$	$e\left(\frac{34}{207}\right)$	$e\left(\frac{215}{414}\right)$	$e\left(\frac{68}{207}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{19}{414}\right)$	$e\left(\frac{283}{414}\right)$	$e\left(\frac{197}{414}\right)$	$e\left(\frac{385}{414}\right)$	$e\left(\frac{8}{207}\right)$	$e\left(\frac{34}{69}\right)$
$\chi_{100016}(75,\cdot)$	100016.vu	276	yes	$-1$	$1$	$e\left(\frac{41}{276}\right)$	$e\left(\frac{247}{276}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{119}{276}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{41}{92}\right)$
$\chi_{100016}(79,\cdot)$	100016.bbo	414	no	$1$	$1$	$e\left(\frac{73}{207}\right)$	$e\left(\frac{37}{207}\right)$	$e\left(\frac{146}{207}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{55}{414}\right)$	$e\left(\frac{110}{207}\right)$	$e\left(\frac{178}{207}\right)$	$e\left(\frac{163}{414}\right)$	$e\left(\frac{74}{207}\right)$	$e\left(\frac{4}{69}\right)$
$\chi_{100016}(81,\cdot)$	100016.vp	207	no	$1$	$1$	$e\left(\frac{1}{207}\right)$	$e\left(\frac{61}{207}\right)$	$e\left(\frac{2}{207}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{119}{207}\right)$	$e\left(\frac{62}{207}\right)$	$e\left(\frac{79}{207}\right)$	$e\left(\frac{167}{207}\right)$	$e\left(\frac{122}{207}\right)$	$e\left(\frac{1}{69}\right)$

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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	$100016$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{6}\times C_{828}\)
Order	$39744$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\(\chi_{100016}(1,\cdot)\)	100016.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{100016}(3,\cdot)\)	100016.bdm	828	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{828}\right)\)	\(e\left(\frac{475}{828}\right)\)	\(e\left(\frac{1}{414}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{119}{828}\right)\)	\(e\left(\frac{119}{207}\right)\)	\(e\left(\frac{143}{414}\right)\)	\(e\left(\frac{197}{207}\right)\)	\(e\left(\frac{61}{414}\right)\)	\(e\left(\frac{1}{276}\right)\)
\(\chi_{100016}(5,\cdot)\)	100016.bdb	828	yes	\(1\)	\(1\)	\(e\left(\frac{475}{828}\right)\)	\(e\left(\frac{547}{828}\right)\)	\(e\left(\frac{61}{414}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{773}{828}\right)\)	\(e\left(\frac{97}{414}\right)\)	\(e\left(\frac{29}{414}\right)\)	\(e\left(\frac{11}{207}\right)\)	\(e\left(\frac{133}{414}\right)\)	\(e\left(\frac{199}{276}\right)\)
\(\chi_{100016}(9,\cdot)\)	100016.yt	414	no	\(1\)	\(1\)	\(e\left(\frac{1}{414}\right)\)	\(e\left(\frac{61}{414}\right)\)	\(e\left(\frac{1}{207}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{119}{414}\right)\)	\(e\left(\frac{31}{207}\right)\)	\(e\left(\frac{143}{207}\right)\)	\(e\left(\frac{187}{207}\right)\)	\(e\left(\frac{61}{207}\right)\)	\(e\left(\frac{1}{138}\right)\)
\(\chi_{100016}(11,\cdot)\)	100016.xa	276	yes	\(1\)	\(1\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{133}{276}\right)\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{81}{92}\right)\)
\(\chi_{100016}(13,\cdot)\)	100016.bca	828	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{828}\right)\)	\(e\left(\frac{773}{828}\right)\)	\(e\left(\frac{119}{414}\right)\)	\(e\left(\frac{209}{276}\right)\)	\(e\left(\frac{637}{828}\right)\)	\(e\left(\frac{16}{207}\right)\)	\(e\left(\frac{43}{414}\right)\)	\(e\left(\frac{52}{207}\right)\)	\(e\left(\frac{359}{414}\right)\)	\(e\left(\frac{119}{276}\right)\)
\(\chi_{100016}(15,\cdot)\)	100016.bat	414	no	\(-1\)	\(1\)	\(e\left(\frac{119}{207}\right)\)	\(e\left(\frac{97}{414}\right)\)	\(e\left(\frac{31}{207}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{16}{207}\right)\)	\(e\left(\frac{335}{414}\right)\)	\(e\left(\frac{86}{207}\right)\)	\(e\left(\frac{1}{207}\right)\)	\(e\left(\frac{97}{207}\right)\)	\(e\left(\frac{50}{69}\right)\)
\(\chi_{100016}(17,\cdot)\)	100016.ban	414	no	\(-1\)	\(1\)	\(e\left(\frac{143}{414}\right)\)	\(e\left(\frac{29}{414}\right)\)	\(e\left(\frac{143}{207}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{43}{414}\right)\)	\(e\left(\frac{86}{207}\right)\)	\(e\left(\frac{119}{414}\right)\)	\(e\left(\frac{38}{207}\right)\)	\(e\left(\frac{29}{207}\right)\)	\(e\left(\frac{5}{138}\right)\)
\(\chi_{100016}(23,\cdot)\)	100016.zj	414	no	\(1\)	\(1\)	\(e\left(\frac{197}{207}\right)\)	\(e\left(\frac{11}{207}\right)\)	\(e\left(\frac{187}{207}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{52}{207}\right)\)	\(e\left(\frac{1}{207}\right)\)	\(e\left(\frac{38}{207}\right)\)	\(e\left(\frac{193}{207}\right)\)	\(e\left(\frac{22}{207}\right)\)	\(e\left(\frac{59}{69}\right)\)
\(\chi_{100016}(25,\cdot)\)	100016.bbh	414	no	\(1\)	\(1\)	\(e\left(\frac{61}{414}\right)\)	\(e\left(\frac{133}{414}\right)\)	\(e\left(\frac{61}{207}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{359}{414}\right)\)	\(e\left(\frac{97}{207}\right)\)	\(e\left(\frac{29}{207}\right)\)	\(e\left(\frac{22}{207}\right)\)	\(e\left(\frac{133}{207}\right)\)	\(e\left(\frac{61}{138}\right)\)
\(\chi_{100016}(27,\cdot)\)	100016.wu	276	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{276}\right)\)	\(e\left(\frac{199}{276}\right)\)	\(e\left(\frac{1}{138}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{119}{276}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{61}{138}\right)\)	\(e\left(\frac{1}{92}\right)\)
\(\chi_{100016}(29,\cdot)\)	100016.bcr	828	no	\(1\)	\(1\)	\(e\left(\frac{617}{828}\right)\)	\(e\left(\frac{515}{828}\right)\)	\(e\left(\frac{203}{414}\right)\)	\(e\left(\frac{113}{276}\right)\)	\(e\left(\frac{283}{828}\right)\)	\(e\left(\frac{76}{207}\right)\)	\(e\left(\frac{128}{207}\right)\)	\(e\left(\frac{40}{207}\right)\)	\(e\left(\frac{101}{414}\right)\)	\(e\left(\frac{65}{276}\right)\)
\(\chi_{100016}(31,\cdot)\)	100016.vl	138	no	\(1\)	\(1\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{43}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{5}{138}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{19}{46}\right)\)
\(\chi_{100016}(33,\cdot)\)	100016.bbk	414	no	\(-1\)	\(1\)	\(e\left(\frac{130}{207}\right)\)	\(e\left(\frac{202}{207}\right)\)	\(e\left(\frac{53}{207}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{373}{414}\right)\)	\(e\left(\frac{125}{207}\right)\)	\(e\left(\frac{47}{414}\right)\)	\(e\left(\frac{157}{414}\right)\)	\(e\left(\frac{197}{207}\right)\)	\(e\left(\frac{61}{69}\right)\)
\(\chi_{100016}(37,\cdot)\)	100016.xj	276	yes	\(-1\)	\(1\)	\(e\left(\frac{233}{276}\right)\)	\(e\left(\frac{229}{276}\right)\)	\(e\left(\frac{95}{138}\right)\)	\(e\left(\frac{269}{276}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{65}{69}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{91}{138}\right)\)	\(e\left(\frac{49}{92}\right)\)
\(\chi_{100016}(39,\cdot)\)	100016.ug	138	no	\(1\)	\(1\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{14}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)
\(\chi_{100016}(41,\cdot)\)	100016.bad	414	no	\(-1\)	\(1\)	\(e\left(\frac{377}{414}\right)\)	\(e\left(\frac{365}{414}\right)\)	\(e\left(\frac{170}{207}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{41}{207}\right)\)	\(e\left(\frac{164}{207}\right)\)	\(e\left(\frac{389}{414}\right)\)	\(e\left(\frac{31}{414}\right)\)	\(e\left(\frac{158}{207}\right)\)	\(e\left(\frac{101}{138}\right)\)
\(\chi_{100016}(43,\cdot)\)	100016.bdf	828	no	\(1\)	\(1\)	\(e\left(\frac{379}{828}\right)\)	\(e\left(\frac{625}{828}\right)\)	\(e\left(\frac{379}{414}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{251}{828}\right)\)	\(e\left(\frac{44}{207}\right)\)	\(e\left(\frac{85}{207}\right)\)	\(e\left(\frac{79}{414}\right)\)	\(e\left(\frac{211}{414}\right)\)	\(e\left(\frac{103}{276}\right)\)
\(\chi_{100016}(45,\cdot)\)	100016.xs	276	yes	\(1\)	\(1\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{223}{276}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{181}{276}\right)\)	\(e\left(\frac{61}{276}\right)\)	\(e\left(\frac{53}{138}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{67}{92}\right)\)
\(\chi_{100016}(51,\cdot)\)	100016.bbz	828	yes	\(1\)	\(1\)	\(e\left(\frac{287}{828}\right)\)	\(e\left(\frac{533}{828}\right)\)	\(e\left(\frac{287}{414}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{205}{828}\right)\)	\(e\left(\frac{205}{207}\right)\)	\(e\left(\frac{131}{207}\right)\)	\(e\left(\frac{28}{207}\right)\)	\(e\left(\frac{119}{414}\right)\)	\(e\left(\frac{11}{276}\right)\)
\(\chi_{100016}(53,\cdot)\)	100016.bcf	828	yes	\(-1\)	\(1\)	\(e\left(\frac{731}{828}\right)\)	\(e\left(\frac{155}{828}\right)\)	\(e\left(\frac{317}{414}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{739}{828}\right)\)	\(e\left(\frac{29}{414}\right)\)	\(e\left(\frac{206}{207}\right)\)	\(e\left(\frac{77}{414}\right)\)	\(e\left(\frac{155}{414}\right)\)	\(e\left(\frac{179}{276}\right)\)
\(\chi_{100016}(55,\cdot)\)	100016.baj	414	no	\(1\)	\(1\)	\(e\left(\frac{83}{414}\right)\)	\(e\left(\frac{13}{207}\right)\)	\(e\left(\frac{83}{207}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{143}{207}\right)\)	\(e\left(\frac{109}{414}\right)\)	\(e\left(\frac{347}{414}\right)\)	\(e\left(\frac{199}{414}\right)\)	\(e\left(\frac{26}{207}\right)\)	\(e\left(\frac{83}{138}\right)\)
\(\chi_{100016}(59,\cdot)\)	100016.bdm	828	yes	\(-1\)	\(1\)	\(e\left(\frac{403}{828}\right)\)	\(e\left(\frac{157}{828}\right)\)	\(e\left(\frac{403}{414}\right)\)	\(e\left(\frac{167}{276}\right)\)	\(e\left(\frac{761}{828}\right)\)	\(e\left(\frac{140}{207}\right)\)	\(e\left(\frac{83}{414}\right)\)	\(e\left(\frac{110}{207}\right)\)	\(e\left(\frac{157}{414}\right)\)	\(e\left(\frac{127}{276}\right)\)
\(\chi_{100016}(61,\cdot)\)	100016.bdg	828	yes	\(-1\)	\(1\)	\(e\left(\frac{221}{828}\right)\)	\(e\left(\frac{647}{828}\right)\)	\(e\left(\frac{221}{414}\right)\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{217}{828}\right)\)	\(e\left(\frac{10}{207}\right)\)	\(e\left(\frac{139}{414}\right)\)	\(e\left(\frac{341}{414}\right)\)	\(e\left(\frac{233}{414}\right)\)	\(e\left(\frac{221}{276}\right)\)
\(\chi_{100016}(65,\cdot)\)	100016.vk	138	no	\(-1\)	\(1\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{7}{46}\right)\)
\(\chi_{100016}(67,\cdot)\)	100016.bce	828	yes	\(-1\)	\(1\)	\(e\left(\frac{647}{828}\right)\)	\(e\left(\frac{827}{828}\right)\)	\(e\left(\frac{233}{414}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{679}{828}\right)\)	\(e\left(\frac{323}{414}\right)\)	\(e\left(\frac{203}{207}\right)\)	\(e\left(\frac{101}{414}\right)\)	\(e\left(\frac{413}{414}\right)\)	\(e\left(\frac{95}{276}\right)\)
\(\chi_{100016}(69,\cdot)\)	100016.wt	276	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{276}\right)\)	\(e\left(\frac{173}{276}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{109}{276}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{73}{138}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{35}{138}\right)\)	\(e\left(\frac{79}{92}\right)\)
\(\chi_{100016}(71,\cdot)\)	100016.bah	414	no	\(1\)	\(1\)	\(e\left(\frac{95}{414}\right)\)	\(e\left(\frac{137}{414}\right)\)	\(e\left(\frac{95}{207}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{29}{207}\right)\)	\(e\left(\frac{116}{207}\right)\)	\(e\left(\frac{130}{207}\right)\)	\(e\left(\frac{133}{414}\right)\)	\(e\left(\frac{137}{207}\right)\)	\(e\left(\frac{95}{138}\right)\)
\(\chi_{100016}(73,\cdot)\)	100016.bao	414	no	\(1\)	\(1\)	\(e\left(\frac{34}{207}\right)\)	\(e\left(\frac{215}{414}\right)\)	\(e\left(\frac{68}{207}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{19}{414}\right)\)	\(e\left(\frac{283}{414}\right)\)	\(e\left(\frac{197}{414}\right)\)	\(e\left(\frac{385}{414}\right)\)	\(e\left(\frac{8}{207}\right)\)	\(e\left(\frac{34}{69}\right)\)
\(\chi_{100016}(75,\cdot)\)	100016.vu	276	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{276}\right)\)	\(e\left(\frac{247}{276}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{119}{276}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{41}{92}\right)\)
\(\chi_{100016}(79,\cdot)\)	100016.bbo	414	no	\(1\)	\(1\)	\(e\left(\frac{73}{207}\right)\)	\(e\left(\frac{37}{207}\right)\)	\(e\left(\frac{146}{207}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{55}{414}\right)\)	\(e\left(\frac{110}{207}\right)\)	\(e\left(\frac{178}{207}\right)\)	\(e\left(\frac{163}{414}\right)\)	\(e\left(\frac{74}{207}\right)\)	\(e\left(\frac{4}{69}\right)\)
\(\chi_{100016}(81,\cdot)\)	100016.vp	207	no	\(1\)	\(1\)	\(e\left(\frac{1}{207}\right)\)	\(e\left(\frac{61}{207}\right)\)	\(e\left(\frac{2}{207}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{119}{207}\right)\)	\(e\left(\frac{62}{207}\right)\)	\(e\left(\frac{79}{207}\right)\)	\(e\left(\frac{167}{207}\right)\)	\(e\left(\frac{122}{207}\right)\)	\(e\left(\frac{1}{69}\right)\)

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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.