LMFDB - Group of Dirichlet characters of modulus 13688

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(13688)

gp:g = idealstar(,13688,2)

magma:G = FullDirichletGroup(13688);

Character group

Order	=	6496	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{812}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{13688}(3423,\cdot)$, $\chi_{13688}(6845,\cdot)$, $\chi_{13688}(5193,\cdot)$, $\chi_{13688}(10209,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 6496 characters

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

Character	Orbit	Order	Primitive	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{13688}(1,\cdot)$	13688.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{13688}(3,\cdot)$	13688.dp	812	yes	$1$	$1$	$e\left(\frac{809}{812}\right)$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{65}{406}\right)$	$e\left(\frac{403}{406}\right)$	$e\left(\frac{13}{812}\right)$	$e\left(\frac{103}{203}\right)$	$e\left(\frac{485}{812}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{297}{812}\right)$	$e\left(\frac{127}{812}\right)$
$\chi_{13688}(5,\cdot)$	13688.dg	406	yes	$1$	$1$	$e\left(\frac{122}{203}\right)$	$e\left(\frac{165}{406}\right)$	$e\left(\frac{59}{203}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{148}{203}\right)$	$e\left(\frac{121}{406}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{181}{203}\right)$
$\chi_{13688}(7,\cdot)$	13688.cz	406	no	$-1$	$1$	$e\left(\frac{65}{406}\right)$	$e\left(\frac{59}{203}\right)$	$e\left(\frac{93}{406}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{395}{406}\right)$	$e\left(\frac{138}{203}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{61}{406}\right)$	$e\left(\frac{79}{203}\right)$
$\chi_{13688}(9,\cdot)$	13688.db	406	no	$1$	$1$	$e\left(\frac{403}{406}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{200}{203}\right)$	$e\left(\frac{13}{406}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{79}{406}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{297}{406}\right)$	$e\left(\frac{127}{406}\right)$
$\chi_{13688}(11,\cdot)$	13688.do	812	yes	$-1$	$1$	$e\left(\frac{13}{812}\right)$	$e\left(\frac{148}{203}\right)$	$e\left(\frac{395}{406}\right)$	$e\left(\frac{13}{406}\right)$	$e\left(\frac{79}{812}\right)$	$e\left(\frac{393}{406}\right)$	$e\left(\frac{605}{812}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{337}{812}\right)$	$e\left(\frac{803}{812}\right)$
$\chi_{13688}(13,\cdot)$	13688.df	406	yes	$-1$	$1$	$e\left(\frac{103}{203}\right)$	$e\left(\frac{121}{406}\right)$	$e\left(\frac{138}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{393}{406}\right)$	$e\left(\frac{200}{203}\right)$	$e\left(\frac{327}{406}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{38}{203}\right)$
$\chi_{13688}(15,\cdot)$	13688.dk	812	no	$1$	$1$	$e\left(\frac{485}{812}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{79}{406}\right)$	$e\left(\frac{605}{812}\right)$	$e\left(\frac{327}{406}\right)$	$e\left(\frac{491}{812}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{705}{812}\right)$	$e\left(\frac{39}{812}\right)$
$\chi_{13688}(17,\cdot)$	13688.cr	116	no	$-1$	$1$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{75}{116}\right)$
$\chi_{13688}(19,\cdot)$	13688.dp	812	yes	$1$	$1$	$e\left(\frac{297}{812}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{61}{406}\right)$	$e\left(\frac{297}{406}\right)$	$e\left(\frac{337}{812}\right)$	$e\left(\frac{156}{203}\right)$	$e\left(\frac{705}{812}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{641}{812}\right)$	$e\left(\frac{419}{812}\right)$
$\chi_{13688}(21,\cdot)$	13688.dr	812	yes	$-1$	$1$	$e\left(\frac{127}{812}\right)$	$e\left(\frac{181}{203}\right)$	$e\left(\frac{79}{203}\right)$	$e\left(\frac{127}{406}\right)$	$e\left(\frac{803}{812}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{39}{812}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{419}{812}\right)$	$e\left(\frac{443}{812}\right)$
$\chi_{13688}(23,\cdot)$	13688.da	406	no	$1$	$1$	$e\left(\frac{1}{406}\right)$	$e\left(\frac{54}{203}\right)$	$e\left(\frac{295}{406}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{167}{203}\right)$	$e\left(\frac{201}{406}\right)$	$e\left(\frac{109}{406}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{307}{406}\right)$	$e\left(\frac{148}{203}\right)$
$\chi_{13688}(25,\cdot)$	13688.cu	203	no	$1$	$1$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{121}{203}\right)$	$e\left(\frac{3}{203}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{159}{203}\right)$
$\chi_{13688}(27,\cdot)$	13688.dp	812	yes	$1$	$1$	$e\left(\frac{803}{812}\right)$	$e\left(\frac{163}{203}\right)$	$e\left(\frac{195}{406}\right)$	$e\left(\frac{397}{406}\right)$	$e\left(\frac{39}{812}\right)$	$e\left(\frac{106}{203}\right)$	$e\left(\frac{643}{812}\right)$	$e\left(\frac{81}{116}\right)$	$e\left(\frac{79}{812}\right)$	$e\left(\frac{381}{812}\right)$
$\chi_{13688}(31,\cdot)$	13688.dl	812	no	$-1$	$1$	$e\left(\frac{747}{812}\right)$	$e\left(\frac{347}{406}\right)$	$e\left(\frac{55}{406}\right)$	$e\left(\frac{341}{406}\right)$	$e\left(\frac{417}{812}\right)$	$e\left(\frac{134}{203}\right)$	$e\left(\frac{629}{812}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{751}{812}\right)$	$e\left(\frac{45}{812}\right)$
$\chi_{13688}(33,\cdot)$	13688.dc	406	no	$-1$	$1$	$e\left(\frac{5}{406}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{27}{203}\right)$	$e\left(\frac{5}{203}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{193}{406}\right)$	$e\left(\frac{139}{406}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{317}{406}\right)$	$e\left(\frac{59}{406}\right)$
$\chi_{13688}(35,\cdot)$	13688.cv	406	yes	$-1$	$1$	$e\left(\frac{309}{406}\right)$	$e\left(\frac{283}{406}\right)$	$e\left(\frac{211}{406}\right)$	$e\left(\frac{106}{203}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{397}{406}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{265}{406}\right)$	$e\left(\frac{57}{203}\right)$
$\chi_{13688}(37,\cdot)$	13688.dq	812	yes	$1$	$1$	$e\left(\frac{365}{812}\right)$	$e\left(\frac{111}{203}\right)$	$e\left(\frac{72}{203}\right)$	$e\left(\frac{365}{406}\right)$	$e\left(\frac{719}{812}\right)$	$e\left(\frac{41}{406}\right)$	$e\left(\frac{809}{812}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{405}{812}\right)$	$e\left(\frac{653}{812}\right)$
$\chi_{13688}(39,\cdot)$	13688.dl	812	no	$-1$	$1$	$e\left(\frac{409}{812}\right)$	$e\left(\frac{365}{406}\right)$	$e\left(\frac{341}{406}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{799}{812}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{327}{812}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{109}{812}\right)$	$e\left(\frac{279}{812}\right)$
$\chi_{13688}(41,\cdot)$	13688.cr	116	no	$-1$	$1$	$e\left(\frac{37}{116}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{77}{116}\right)$
$\chi_{13688}(43,\cdot)$	13688.do	812	yes	$-1$	$1$	$e\left(\frac{625}{812}\right)$	$e\left(\frac{26}{203}\right)$	$e\left(\frac{127}{406}\right)$	$e\left(\frac{219}{406}\right)$	$e\left(\frac{675}{812}\right)$	$e\left(\frac{187}{406}\right)$	$e\left(\frac{729}{812}\right)$	$e\left(\frac{59}{116}\right)$	$e\left(\frac{649}{812}\right)$	$e\left(\frac{67}{812}\right)$
$\chi_{13688}(45,\cdot)$	13688.cx	406	yes	$1$	$1$	$e\left(\frac{241}{406}\right)$	$e\left(\frac{247}{406}\right)$	$e\left(\frac{124}{203}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{309}{406}\right)$	$e\left(\frac{127}{406}\right)$	$e\left(\frac{41}{203}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{95}{406}\right)$	$e\left(\frac{83}{406}\right)$
$\chi_{13688}(47,\cdot)$	13688.dl	812	no	$-1$	$1$	$e\left(\frac{237}{812}\right)$	$e\left(\frac{9}{406}\right)$	$e\left(\frac{143}{406}\right)$	$e\left(\frac{237}{406}\right)$	$e\left(\frac{191}{812}\right)$	$e\left(\frac{186}{203}\right)$	$e\left(\frac{255}{812}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{85}{812}\right)$	$e\left(\frac{523}{812}\right)$
$\chi_{13688}(49,\cdot)$	13688.cu	203	no	$1$	$1$	$e\left(\frac{65}{203}\right)$	$e\left(\frac{118}{203}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{130}{203}\right)$	$e\left(\frac{192}{203}\right)$	$e\left(\frac{73}{203}\right)$	$e\left(\frac{183}{203}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{61}{203}\right)$	$e\left(\frac{158}{203}\right)$
$\chi_{13688}(51,\cdot)$	13688.cv	406	yes	$-1$	$1$	$e\left(\frac{93}{406}\right)$	$e\left(\frac{97}{406}\right)$	$e\left(\frac{233}{406}\right)$	$e\left(\frac{93}{203}\right)$	$e\left(\frac{3}{406}\right)$	$e\left(\frac{17}{406}\right)$	$e\left(\frac{95}{203}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{131}{406}\right)$	$e\left(\frac{163}{203}\right)$
$\chi_{13688}(53,\cdot)$	13688.cx	406	yes	$1$	$1$	$e\left(\frac{363}{406}\right)$	$e\left(\frac{25}{406}\right)$	$e\left(\frac{52}{203}\right)$	$e\left(\frac{160}{203}\right)$	$e\left(\frac{51}{406}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{194}{203}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{197}{406}\right)$	$e\left(\frac{61}{406}\right)$
$\chi_{13688}(55,\cdot)$	13688.dl	812	no	$-1$	$1$	$e\left(\frac{501}{812}\right)$	$e\left(\frac{55}{406}\right)$	$e\left(\frac{107}{406}\right)$	$e\left(\frac{95}{406}\right)$	$e\left(\frac{671}{812}\right)$	$e\left(\frac{54}{203}\right)$	$e\left(\frac{611}{812}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{745}{812}\right)$	$e\left(\frac{715}{812}\right)$
$\chi_{13688}(57,\cdot)$	13688.cf	58	no	$1$	$1$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{39}{58}\right)$
$\chi_{13688}(61,\cdot)$	13688.dq	812	yes	$1$	$1$	$e\left(\frac{207}{812}\right)$	$e\left(\frac{108}{203}\right)$	$e\left(\frac{92}{203}\right)$	$e\left(\frac{207}{406}\right)$	$e\left(\frac{321}{812}\right)$	$e\left(\frac{199}{406}\right)$	$e\left(\frac{639}{812}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{619}{812}\right)$	$e\left(\frac{575}{812}\right)$
$\chi_{13688}(63,\cdot)$	13688.di	406	no	$-1$	$1$	$e\left(\frac{31}{203}\right)$	$e\left(\frac{100}{203}\right)$	$e\left(\frac{223}{406}\right)$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{1}{203}\right)$	$e\left(\frac{141}{203}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{179}{203}\right)$	$e\left(\frac{285}{406}\right)$
$\chi_{13688}(65,\cdot)$	13688.dj	406	no	$-1$	$1$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{143}{203}\right)$	$e\left(\frac{197}{203}\right)$	$e\left(\frac{44}{203}\right)$	$e\left(\frac{283}{406}\right)$	$e\left(\frac{115}{406}\right)$	$e\left(\frac{165}{203}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{55}{203}\right)$	$e\left(\frac{16}{203}\right)$
$\chi_{13688}(67,\cdot)$	13688.cw	406	yes	$1$	$1$	$e\left(\frac{151}{406}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{291}{406}\right)$	$e\left(\frac{151}{203}\right)$	$e\left(\frac{45}{203}\right)$	$e\left(\frac{52}{203}\right)$	$e\left(\frac{8}{203}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{73}{406}\right)$	$e\left(\frac{18}{203}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$13688$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{812}\)
Order	$6496$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{13688}(1,\cdot)\)	13688.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{13688}(3,\cdot)\)	13688.dp	812	yes	\(1\)	\(1\)	\(e\left(\frac{809}{812}\right)\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{65}{406}\right)\)	\(e\left(\frac{403}{406}\right)\)	\(e\left(\frac{13}{812}\right)\)	\(e\left(\frac{103}{203}\right)\)	\(e\left(\frac{485}{812}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{297}{812}\right)\)	\(e\left(\frac{127}{812}\right)\)
\(\chi_{13688}(5,\cdot)\)	13688.dg	406	yes	\(1\)	\(1\)	\(e\left(\frac{122}{203}\right)\)	\(e\left(\frac{165}{406}\right)\)	\(e\left(\frac{59}{203}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{148}{203}\right)\)	\(e\left(\frac{121}{406}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{181}{203}\right)\)
\(\chi_{13688}(7,\cdot)\)	13688.cz	406	no	\(-1\)	\(1\)	\(e\left(\frac{65}{406}\right)\)	\(e\left(\frac{59}{203}\right)\)	\(e\left(\frac{93}{406}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{395}{406}\right)\)	\(e\left(\frac{138}{203}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{61}{406}\right)\)	\(e\left(\frac{79}{203}\right)\)
\(\chi_{13688}(9,\cdot)\)	13688.db	406	no	\(1\)	\(1\)	\(e\left(\frac{403}{406}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{200}{203}\right)\)	\(e\left(\frac{13}{406}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{79}{406}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{297}{406}\right)\)	\(e\left(\frac{127}{406}\right)\)
\(\chi_{13688}(11,\cdot)\)	13688.do	812	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{812}\right)\)	\(e\left(\frac{148}{203}\right)\)	\(e\left(\frac{395}{406}\right)\)	\(e\left(\frac{13}{406}\right)\)	\(e\left(\frac{79}{812}\right)\)	\(e\left(\frac{393}{406}\right)\)	\(e\left(\frac{605}{812}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{337}{812}\right)\)	\(e\left(\frac{803}{812}\right)\)
\(\chi_{13688}(13,\cdot)\)	13688.df	406	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{203}\right)\)	\(e\left(\frac{121}{406}\right)\)	\(e\left(\frac{138}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{393}{406}\right)\)	\(e\left(\frac{200}{203}\right)\)	\(e\left(\frac{327}{406}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{38}{203}\right)\)
\(\chi_{13688}(15,\cdot)\)	13688.dk	812	no	\(1\)	\(1\)	\(e\left(\frac{485}{812}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{79}{406}\right)\)	\(e\left(\frac{605}{812}\right)\)	\(e\left(\frac{327}{406}\right)\)	\(e\left(\frac{491}{812}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{705}{812}\right)\)	\(e\left(\frac{39}{812}\right)\)
\(\chi_{13688}(17,\cdot)\)	13688.cr	116	no	\(-1\)	\(1\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{75}{116}\right)\)
\(\chi_{13688}(19,\cdot)\)	13688.dp	812	yes	\(1\)	\(1\)	\(e\left(\frac{297}{812}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{61}{406}\right)\)	\(e\left(\frac{297}{406}\right)\)	\(e\left(\frac{337}{812}\right)\)	\(e\left(\frac{156}{203}\right)\)	\(e\left(\frac{705}{812}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{641}{812}\right)\)	\(e\left(\frac{419}{812}\right)\)
\(\chi_{13688}(21,\cdot)\)	13688.dr	812	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{812}\right)\)	\(e\left(\frac{181}{203}\right)\)	\(e\left(\frac{79}{203}\right)\)	\(e\left(\frac{127}{406}\right)\)	\(e\left(\frac{803}{812}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{39}{812}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{419}{812}\right)\)	\(e\left(\frac{443}{812}\right)\)
\(\chi_{13688}(23,\cdot)\)	13688.da	406	no	\(1\)	\(1\)	\(e\left(\frac{1}{406}\right)\)	\(e\left(\frac{54}{203}\right)\)	\(e\left(\frac{295}{406}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{167}{203}\right)\)	\(e\left(\frac{201}{406}\right)\)	\(e\left(\frac{109}{406}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{307}{406}\right)\)	\(e\left(\frac{148}{203}\right)\)
\(\chi_{13688}(25,\cdot)\)	13688.cu	203	no	\(1\)	\(1\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{82}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{121}{203}\right)\)	\(e\left(\frac{3}{203}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{159}{203}\right)\)
\(\chi_{13688}(27,\cdot)\)	13688.dp	812	yes	\(1\)	\(1\)	\(e\left(\frac{803}{812}\right)\)	\(e\left(\frac{163}{203}\right)\)	\(e\left(\frac{195}{406}\right)\)	\(e\left(\frac{397}{406}\right)\)	\(e\left(\frac{39}{812}\right)\)	\(e\left(\frac{106}{203}\right)\)	\(e\left(\frac{643}{812}\right)\)	\(e\left(\frac{81}{116}\right)\)	\(e\left(\frac{79}{812}\right)\)	\(e\left(\frac{381}{812}\right)\)
\(\chi_{13688}(31,\cdot)\)	13688.dl	812	no	\(-1\)	\(1\)	\(e\left(\frac{747}{812}\right)\)	\(e\left(\frac{347}{406}\right)\)	\(e\left(\frac{55}{406}\right)\)	\(e\left(\frac{341}{406}\right)\)	\(e\left(\frac{417}{812}\right)\)	\(e\left(\frac{134}{203}\right)\)	\(e\left(\frac{629}{812}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{751}{812}\right)\)	\(e\left(\frac{45}{812}\right)\)
\(\chi_{13688}(33,\cdot)\)	13688.dc	406	no	\(-1\)	\(1\)	\(e\left(\frac{5}{406}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{27}{203}\right)\)	\(e\left(\frac{5}{203}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{193}{406}\right)\)	\(e\left(\frac{139}{406}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{317}{406}\right)\)	\(e\left(\frac{59}{406}\right)\)
\(\chi_{13688}(35,\cdot)\)	13688.cv	406	yes	\(-1\)	\(1\)	\(e\left(\frac{309}{406}\right)\)	\(e\left(\frac{283}{406}\right)\)	\(e\left(\frac{211}{406}\right)\)	\(e\left(\frac{106}{203}\right)\)	\(e\left(\frac{285}{406}\right)\)	\(e\left(\frac{397}{406}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{265}{406}\right)\)	\(e\left(\frac{57}{203}\right)\)
\(\chi_{13688}(37,\cdot)\)	13688.dq	812	yes	\(1\)	\(1\)	\(e\left(\frac{365}{812}\right)\)	\(e\left(\frac{111}{203}\right)\)	\(e\left(\frac{72}{203}\right)\)	\(e\left(\frac{365}{406}\right)\)	\(e\left(\frac{719}{812}\right)\)	\(e\left(\frac{41}{406}\right)\)	\(e\left(\frac{809}{812}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{405}{812}\right)\)	\(e\left(\frac{653}{812}\right)\)
\(\chi_{13688}(39,\cdot)\)	13688.dl	812	no	\(-1\)	\(1\)	\(e\left(\frac{409}{812}\right)\)	\(e\left(\frac{365}{406}\right)\)	\(e\left(\frac{341}{406}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{799}{812}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{327}{812}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{109}{812}\right)\)	\(e\left(\frac{279}{812}\right)\)
\(\chi_{13688}(41,\cdot)\)	13688.cr	116	no	\(-1\)	\(1\)	\(e\left(\frac{37}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{77}{116}\right)\)
\(\chi_{13688}(43,\cdot)\)	13688.do	812	yes	\(-1\)	\(1\)	\(e\left(\frac{625}{812}\right)\)	\(e\left(\frac{26}{203}\right)\)	\(e\left(\frac{127}{406}\right)\)	\(e\left(\frac{219}{406}\right)\)	\(e\left(\frac{675}{812}\right)\)	\(e\left(\frac{187}{406}\right)\)	\(e\left(\frac{729}{812}\right)\)	\(e\left(\frac{59}{116}\right)\)	\(e\left(\frac{649}{812}\right)\)	\(e\left(\frac{67}{812}\right)\)
\(\chi_{13688}(45,\cdot)\)	13688.cx	406	yes	\(1\)	\(1\)	\(e\left(\frac{241}{406}\right)\)	\(e\left(\frac{247}{406}\right)\)	\(e\left(\frac{124}{203}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{309}{406}\right)\)	\(e\left(\frac{127}{406}\right)\)	\(e\left(\frac{41}{203}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{95}{406}\right)\)	\(e\left(\frac{83}{406}\right)\)
\(\chi_{13688}(47,\cdot)\)	13688.dl	812	no	\(-1\)	\(1\)	\(e\left(\frac{237}{812}\right)\)	\(e\left(\frac{9}{406}\right)\)	\(e\left(\frac{143}{406}\right)\)	\(e\left(\frac{237}{406}\right)\)	\(e\left(\frac{191}{812}\right)\)	\(e\left(\frac{186}{203}\right)\)	\(e\left(\frac{255}{812}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{85}{812}\right)\)	\(e\left(\frac{523}{812}\right)\)
\(\chi_{13688}(49,\cdot)\)	13688.cu	203	no	\(1\)	\(1\)	\(e\left(\frac{65}{203}\right)\)	\(e\left(\frac{118}{203}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{130}{203}\right)\)	\(e\left(\frac{192}{203}\right)\)	\(e\left(\frac{73}{203}\right)\)	\(e\left(\frac{183}{203}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{61}{203}\right)\)	\(e\left(\frac{158}{203}\right)\)
\(\chi_{13688}(51,\cdot)\)	13688.cv	406	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{406}\right)\)	\(e\left(\frac{97}{406}\right)\)	\(e\left(\frac{233}{406}\right)\)	\(e\left(\frac{93}{203}\right)\)	\(e\left(\frac{3}{406}\right)\)	\(e\left(\frac{17}{406}\right)\)	\(e\left(\frac{95}{203}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{131}{406}\right)\)	\(e\left(\frac{163}{203}\right)\)
\(\chi_{13688}(53,\cdot)\)	13688.cx	406	yes	\(1\)	\(1\)	\(e\left(\frac{363}{406}\right)\)	\(e\left(\frac{25}{406}\right)\)	\(e\left(\frac{52}{203}\right)\)	\(e\left(\frac{160}{203}\right)\)	\(e\left(\frac{51}{406}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{194}{203}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{197}{406}\right)\)	\(e\left(\frac{61}{406}\right)\)
\(\chi_{13688}(55,\cdot)\)	13688.dl	812	no	\(-1\)	\(1\)	\(e\left(\frac{501}{812}\right)\)	\(e\left(\frac{55}{406}\right)\)	\(e\left(\frac{107}{406}\right)\)	\(e\left(\frac{95}{406}\right)\)	\(e\left(\frac{671}{812}\right)\)	\(e\left(\frac{54}{203}\right)\)	\(e\left(\frac{611}{812}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{745}{812}\right)\)	\(e\left(\frac{715}{812}\right)\)
\(\chi_{13688}(57,\cdot)\)	13688.cf	58	no	\(1\)	\(1\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)
\(\chi_{13688}(61,\cdot)\)	13688.dq	812	yes	\(1\)	\(1\)	\(e\left(\frac{207}{812}\right)\)	\(e\left(\frac{108}{203}\right)\)	\(e\left(\frac{92}{203}\right)\)	\(e\left(\frac{207}{406}\right)\)	\(e\left(\frac{321}{812}\right)\)	\(e\left(\frac{199}{406}\right)\)	\(e\left(\frac{639}{812}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{619}{812}\right)\)	\(e\left(\frac{575}{812}\right)\)
\(\chi_{13688}(63,\cdot)\)	13688.di	406	no	\(-1\)	\(1\)	\(e\left(\frac{31}{203}\right)\)	\(e\left(\frac{100}{203}\right)\)	\(e\left(\frac{223}{406}\right)\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{1}{203}\right)\)	\(e\left(\frac{141}{203}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{179}{203}\right)\)	\(e\left(\frac{285}{406}\right)\)
\(\chi_{13688}(65,\cdot)\)	13688.dj	406	no	\(-1\)	\(1\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{143}{203}\right)\)	\(e\left(\frac{197}{203}\right)\)	\(e\left(\frac{44}{203}\right)\)	\(e\left(\frac{283}{406}\right)\)	\(e\left(\frac{115}{406}\right)\)	\(e\left(\frac{165}{203}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{55}{203}\right)\)	\(e\left(\frac{16}{203}\right)\)
\(\chi_{13688}(67,\cdot)\)	13688.cw	406	yes	\(1\)	\(1\)	\(e\left(\frac{151}{406}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{291}{406}\right)\)	\(e\left(\frac{151}{203}\right)\)	\(e\left(\frac{45}{203}\right)\)	\(e\left(\frac{52}{203}\right)\)	\(e\left(\frac{8}{203}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{73}{406}\right)\)	\(e\left(\frac{18}{203}\right)\)

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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.