LMFDB - Group of Dirichlet characters of modulus 8061

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(8061)

gp:g = idealstar(,8061,2)

magma:G = FullDirichletGroup(8061);

Character group

Order	=	5372	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2686}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{8061}(5375,\cdot)$, $\chi_{8061}(2692,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 5372 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8061}(1,\cdot)$	8061.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8061}(2,\cdot)$	8061.l	158	yes	$-1$	$1$	$e\left(\frac{39}{158}\right)$	$e\left(\frac{39}{79}\right)$	$e\left(\frac{133}{158}\right)$	$e\left(\frac{10}{79}\right)$	$e\left(\frac{117}{158}\right)$	$e\left(\frac{7}{79}\right)$	$e\left(\frac{23}{158}\right)$	$e\left(\frac{9}{79}\right)$	$e\left(\frac{59}{158}\right)$	$e\left(\frac{78}{79}\right)$
$\chi_{8061}(4,\cdot)$	8061.i	79	no	$1$	$1$	$e\left(\frac{39}{79}\right)$	$e\left(\frac{78}{79}\right)$	$e\left(\frac{54}{79}\right)$	$e\left(\frac{20}{79}\right)$	$e\left(\frac{38}{79}\right)$	$e\left(\frac{14}{79}\right)$	$e\left(\frac{23}{79}\right)$	$e\left(\frac{18}{79}\right)$	$e\left(\frac{59}{79}\right)$	$e\left(\frac{77}{79}\right)$
$\chi_{8061}(5,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{133}{158}\right)$	$e\left(\frac{54}{79}\right)$	$e\left(\frac{672}{1343}\right)$	$e\left(\frac{205}{1343}\right)$	$e\left(\frac{83}{158}\right)$	$e\left(\frac{919}{2686}\right)$	$e\left(\frac{295}{1343}\right)$	$e\left(\frac{66}{1343}\right)$	$e\left(\frac{2671}{2686}\right)$	$e\left(\frac{29}{79}\right)$
$\chi_{8061}(7,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{10}{79}\right)$	$e\left(\frac{20}{79}\right)$	$e\left(\frac{205}{1343}\right)$	$e\left(\frac{784}{1343}\right)$	$e\left(\frac{30}{79}\right)$	$e\left(\frac{375}{1343}\right)$	$e\left(\frac{80}{1343}\right)$	$e\left(\frac{200}{1343}\right)$	$e\left(\frac{954}{1343}\right)$	$e\left(\frac{40}{79}\right)$
$\chi_{8061}(8,\cdot)$	8061.l	158	yes	$-1$	$1$	$e\left(\frac{117}{158}\right)$	$e\left(\frac{38}{79}\right)$	$e\left(\frac{83}{158}\right)$	$e\left(\frac{30}{79}\right)$	$e\left(\frac{35}{158}\right)$	$e\left(\frac{21}{79}\right)$	$e\left(\frac{69}{158}\right)$	$e\left(\frac{27}{79}\right)$	$e\left(\frac{19}{158}\right)$	$e\left(\frac{76}{79}\right)$
$\chi_{8061}(10,\cdot)$	8061.n	2686	no	$-1$	$1$	$e\left(\frac{7}{79}\right)$	$e\left(\frac{14}{79}\right)$	$e\left(\frac{919}{2686}\right)$	$e\left(\frac{375}{1343}\right)$	$e\left(\frac{21}{79}\right)$	$e\left(\frac{1157}{2686}\right)$	$e\left(\frac{981}{2686}\right)$	$e\left(\frac{219}{1343}\right)$	$e\left(\frac{494}{1343}\right)$	$e\left(\frac{28}{79}\right)$
$\chi_{8061}(11,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{23}{158}\right)$	$e\left(\frac{23}{79}\right)$	$e\left(\frac{295}{1343}\right)$	$e\left(\frac{80}{1343}\right)$	$e\left(\frac{69}{158}\right)$	$e\left(\frac{981}{2686}\right)$	$e\left(\frac{803}{1343}\right)$	$e\left(\frac{1336}{1343}\right)$	$e\left(\frac{551}{2686}\right)$	$e\left(\frac{46}{79}\right)$
$\chi_{8061}(13,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{9}{79}\right)$	$e\left(\frac{18}{79}\right)$	$e\left(\frac{66}{1343}\right)$	$e\left(\frac{200}{1343}\right)$	$e\left(\frac{27}{79}\right)$	$e\left(\frac{219}{1343}\right)$	$e\left(\frac{1336}{1343}\right)$	$e\left(\frac{654}{1343}\right)$	$e\left(\frac{353}{1343}\right)$	$e\left(\frac{36}{79}\right)$
$\chi_{8061}(14,\cdot)$	8061.o	2686	yes	$-1$	$1$	$e\left(\frac{59}{158}\right)$	$e\left(\frac{59}{79}\right)$	$e\left(\frac{2671}{2686}\right)$	$e\left(\frac{954}{1343}\right)$	$e\left(\frac{19}{158}\right)$	$e\left(\frac{494}{1343}\right)$	$e\left(\frac{551}{2686}\right)$	$e\left(\frac{353}{1343}\right)$	$e\left(\frac{225}{2686}\right)$	$e\left(\frac{39}{79}\right)$
$\chi_{8061}(16,\cdot)$	8061.i	79	no	$1$	$1$	$e\left(\frac{78}{79}\right)$	$e\left(\frac{77}{79}\right)$	$e\left(\frac{29}{79}\right)$	$e\left(\frac{40}{79}\right)$	$e\left(\frac{76}{79}\right)$	$e\left(\frac{28}{79}\right)$	$e\left(\frac{46}{79}\right)$	$e\left(\frac{36}{79}\right)$	$e\left(\frac{39}{79}\right)$	$e\left(\frac{75}{79}\right)$
$\chi_{8061}(17,\cdot)$	8061.o	2686	yes	$-1$	$1$	$e\left(\frac{113}{158}\right)$	$e\left(\frac{34}{79}\right)$	$e\left(\frac{2593}{2686}\right)$	$e\left(\frac{1080}{1343}\right)$	$e\left(\frac{23}{158}\right)$	$e\left(\frac{914}{1343}\right)$	$e\left(\frac{193}{2686}\right)$	$e\left(\frac{577}{1343}\right)$	$e\left(\frac{1395}{2686}\right)$	$e\left(\frac{68}{79}\right)$
$\chi_{8061}(19,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{77}{79}\right)$	$e\left(\frac{75}{79}\right)$	$e\left(\frac{38}{1343}\right)$	$e\left(\frac{807}{1343}\right)$	$e\left(\frac{73}{79}\right)$	$e\left(\frac{4}{1343}\right)$	$e\left(\frac{932}{1343}\right)$	$e\left(\frac{987}{1343}\right)$	$e\left(\frac{773}{1343}\right)$	$e\left(\frac{71}{79}\right)$
$\chi_{8061}(20,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{53}{158}\right)$	$e\left(\frac{53}{79}\right)$	$e\left(\frac{247}{1343}\right)$	$e\left(\frac{545}{1343}\right)$	$e\left(\frac{1}{158}\right)$	$e\left(\frac{1395}{2686}\right)$	$e\left(\frac{686}{1343}\right)$	$e\left(\frac{372}{1343}\right)$	$e\left(\frac{1991}{2686}\right)$	$e\left(\frac{27}{79}\right)$
$\chi_{8061}(22,\cdot)$	8061.n	2686	no	$-1$	$1$	$e\left(\frac{31}{79}\right)$	$e\left(\frac{62}{79}\right)$	$e\left(\frac{165}{2686}\right)$	$e\left(\frac{250}{1343}\right)$	$e\left(\frac{14}{79}\right)$	$e\left(\frac{1219}{2686}\right)$	$e\left(\frac{1997}{2686}\right)$	$e\left(\frac{146}{1343}\right)$	$e\left(\frac{777}{1343}\right)$	$e\left(\frac{45}{79}\right)$
$\chi_{8061}(23,\cdot)$	8061.o	2686	yes	$-1$	$1$	$e\left(\frac{93}{158}\right)$	$e\left(\frac{14}{79}\right)$	$e\left(\frac{603}{2686}\right)$	$e\left(\frac{59}{1343}\right)$	$e\left(\frac{121}{158}\right)$	$e\left(\frac{1092}{1343}\right)$	$e\left(\frac{2561}{2686}\right)$	$e\left(\frac{851}{1343}\right)$	$e\left(\frac{1699}{2686}\right)$	$e\left(\frac{28}{79}\right)$
$\chi_{8061}(25,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{54}{79}\right)$	$e\left(\frac{29}{79}\right)$	$e\left(\frac{1}{1343}\right)$	$e\left(\frac{410}{1343}\right)$	$e\left(\frac{4}{79}\right)$	$e\left(\frac{919}{1343}\right)$	$e\left(\frac{590}{1343}\right)$	$e\left(\frac{132}{1343}\right)$	$e\left(\frac{1328}{1343}\right)$	$e\left(\frac{58}{79}\right)$
$\chi_{8061}(26,\cdot)$	8061.o	2686	yes	$-1$	$1$	$e\left(\frac{57}{158}\right)$	$e\left(\frac{57}{79}\right)$	$e\left(\frac{2393}{2686}\right)$	$e\left(\frac{370}{1343}\right)$	$e\left(\frac{13}{158}\right)$	$e\left(\frac{338}{1343}\right)$	$e\left(\frac{377}{2686}\right)$	$e\left(\frac{807}{1343}\right)$	$e\left(\frac{1709}{2686}\right)$	$e\left(\frac{35}{79}\right)$
$\chi_{8061}(28,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{49}{79}\right)$	$e\left(\frac{19}{79}\right)$	$e\left(\frac{1123}{1343}\right)$	$e\left(\frac{1124}{1343}\right)$	$e\left(\frac{68}{79}\right)$	$e\left(\frac{613}{1343}\right)$	$e\left(\frac{471}{1343}\right)$	$e\left(\frac{506}{1343}\right)$	$e\left(\frac{614}{1343}\right)$	$e\left(\frac{38}{79}\right)$
$\chi_{8061}(29,\cdot)$	8061.k	158	yes	$1$	$1$	$e\left(\frac{141}{158}\right)$	$e\left(\frac{62}{79}\right)$	$e\left(\frac{49}{79}\right)$	$e\left(\frac{24}{79}\right)$	$e\left(\frac{107}{158}\right)$	$e\left(\frac{81}{158}\right)$	$e\left(\frac{75}{79}\right)$	$e\left(\frac{69}{79}\right)$	$e\left(\frac{31}{158}\right)$	$e\left(\frac{45}{79}\right)$
$\chi_{8061}(31,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{4}{79}\right)$	$e\left(\frac{8}{79}\right)$	$e\left(\frac{1030}{1343}\right)$	$e\left(\frac{598}{1343}\right)$	$e\left(\frac{12}{79}\right)$	$e\left(\frac{1098}{1343}\right)$	$e\left(\frac{664}{1343}\right)$	$e\left(\frac{317}{1343}\right)$	$e\left(\frac{666}{1343}\right)$	$e\left(\frac{16}{79}\right)$
$\chi_{8061}(32,\cdot)$	8061.l	158	yes	$-1$	$1$	$e\left(\frac{37}{158}\right)$	$e\left(\frac{37}{79}\right)$	$e\left(\frac{33}{158}\right)$	$e\left(\frac{50}{79}\right)$	$e\left(\frac{111}{158}\right)$	$e\left(\frac{35}{79}\right)$	$e\left(\frac{115}{158}\right)$	$e\left(\frac{45}{79}\right)$	$e\left(\frac{137}{158}\right)$	$e\left(\frac{74}{79}\right)$
$\chi_{8061}(34,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{76}{79}\right)$	$e\left(\frac{73}{79}\right)$	$e\left(\frac{1084}{1343}\right)$	$e\left(\frac{1250}{1343}\right)$	$e\left(\frac{70}{79}\right)$	$e\left(\frac{1033}{1343}\right)$	$e\left(\frac{292}{1343}\right)$	$e\left(\frac{730}{1343}\right)$	$e\left(\frac{1199}{1343}\right)$	$e\left(\frac{67}{79}\right)$
$\chi_{8061}(35,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{153}{158}\right)$	$e\left(\frac{74}{79}\right)$	$e\left(\frac{877}{1343}\right)$	$e\left(\frac{989}{1343}\right)$	$e\left(\frac{143}{158}\right)$	$e\left(\frac{1669}{2686}\right)$	$e\left(\frac{375}{1343}\right)$	$e\left(\frac{266}{1343}\right)$	$e\left(\frac{1893}{2686}\right)$	$e\left(\frac{69}{79}\right)$
$\chi_{8061}(37,\cdot)$	8061.n	2686	no	$-1$	$1$	$e\left(\frac{44}{79}\right)$	$e\left(\frac{9}{79}\right)$	$e\left(\frac{777}{2686}\right)$	$e\left(\frac{811}{1343}\right)$	$e\left(\frac{53}{79}\right)$	$e\left(\frac{2273}{2686}\right)$	$e\left(\frac{467}{2686}\right)$	$e\left(\frac{248}{1343}\right)$	$e\left(\frac{216}{1343}\right)$	$e\left(\frac{18}{79}\right)$
$\chi_{8061}(38,\cdot)$	8061.o	2686	yes	$-1$	$1$	$e\left(\frac{35}{158}\right)$	$e\left(\frac{35}{79}\right)$	$e\left(\frac{2337}{2686}\right)$	$e\left(\frac{977}{1343}\right)$	$e\left(\frac{105}{158}\right)$	$e\left(\frac{123}{1343}\right)$	$e\left(\frac{2255}{2686}\right)$	$e\left(\frac{1140}{1343}\right)$	$e\left(\frac{2549}{2686}\right)$	$e\left(\frac{70}{79}\right)$
$\chi_{8061}(40,\cdot)$	8061.n	2686	no	$-1$	$1$	$e\left(\frac{46}{79}\right)$	$e\left(\frac{13}{79}\right)$	$e\left(\frac{69}{2686}\right)$	$e\left(\frac{715}{1343}\right)$	$e\left(\frac{59}{79}\right)$	$e\left(\frac{1633}{2686}\right)$	$e\left(\frac{1763}{2686}\right)$	$e\left(\frac{525}{1343}\right)$	$e\left(\frac{154}{1343}\right)$	$e\left(\frac{26}{79}\right)$
$\chi_{8061}(41,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{69}{158}\right)$	$e\left(\frac{69}{79}\right)$	$e\left(\frac{16}{1343}\right)$	$e\left(\frac{1188}{1343}\right)$	$e\left(\frac{49}{158}\right)$	$e\left(\frac{1205}{2686}\right)$	$e\left(\frac{39}{1343}\right)$	$e\left(\frac{769}{1343}\right)$	$e\left(\frac{863}{2686}\right)$	$e\left(\frac{59}{79}\right)$
$\chi_{8061}(43,\cdot)$	8061.n	2686	no	$-1$	$1$	$e\left(\frac{77}{79}\right)$	$e\left(\frac{75}{79}\right)$	$e\left(\frac{2683}{2686}\right)$	$e\left(\frac{728}{1343}\right)$	$e\left(\frac{73}{79}\right)$	$e\left(\frac{2615}{2686}\right)$	$e\left(\frac{2259}{2686}\right)$	$e\left(\frac{1145}{1343}\right)$	$e\left(\frac{694}{1343}\right)$	$e\left(\frac{71}{79}\right)$
$\chi_{8061}(44,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{101}{158}\right)$	$e\left(\frac{22}{79}\right)$	$e\left(\frac{1213}{1343}\right)$	$e\left(\frac{420}{1343}\right)$	$e\left(\frac{145}{158}\right)$	$e\left(\frac{1457}{2686}\right)$	$e\left(\frac{1194}{1343}\right)$	$e\left(\frac{299}{1343}\right)$	$e\left(\frac{2557}{2686}\right)$	$e\left(\frac{44}{79}\right)$
$\chi_{8061}(46,\cdot)$	8061.m	1343	no	$1$	$1$	$e\left(\frac{66}{79}\right)$	$e\left(\frac{53}{79}\right)$	$e\left(\frac{89}{1343}\right)$	$e\left(\frac{229}{1343}\right)$	$e\left(\frac{40}{79}\right)$	$e\left(\frac{1211}{1343}\right)$	$e\left(\frac{133}{1343}\right)$	$e\left(\frac{1004}{1343}\right)$	$e\left(\frac{8}{1343}\right)$	$e\left(\frac{27}{79}\right)$
$\chi_{8061}(47,\cdot)$	8061.p	2686	yes	$1$	$1$	$e\left(\frac{19}{158}\right)$	$e\left(\frac{19}{79}\right)$	$e\left(\frac{728}{1343}\right)$	$e\left(\frac{334}{1343}\right)$	$e\left(\frac{57}{158}\right)$	$e\left(\frac{1779}{2686}\right)$	$e\left(\frac{1103}{1343}\right)$	$e\left(\frac{743}{1343}\right)$	$e\left(\frac{991}{2686}\right)$	$e\left(\frac{38}{79}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$8061$
Structure	\(C_{2}\times C_{2686}\)
Order	$5372$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8061}(1,\cdot)\)	8061.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8061}(2,\cdot)\)	8061.l	158	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{158}\right)\)	\(e\left(\frac{39}{79}\right)\)	\(e\left(\frac{133}{158}\right)\)	\(e\left(\frac{10}{79}\right)\)	\(e\left(\frac{117}{158}\right)\)	\(e\left(\frac{7}{79}\right)\)	\(e\left(\frac{23}{158}\right)\)	\(e\left(\frac{9}{79}\right)\)	\(e\left(\frac{59}{158}\right)\)	\(e\left(\frac{78}{79}\right)\)
\(\chi_{8061}(4,\cdot)\)	8061.i	79	no	\(1\)	\(1\)	\(e\left(\frac{39}{79}\right)\)	\(e\left(\frac{78}{79}\right)\)	\(e\left(\frac{54}{79}\right)\)	\(e\left(\frac{20}{79}\right)\)	\(e\left(\frac{38}{79}\right)\)	\(e\left(\frac{14}{79}\right)\)	\(e\left(\frac{23}{79}\right)\)	\(e\left(\frac{18}{79}\right)\)	\(e\left(\frac{59}{79}\right)\)	\(e\left(\frac{77}{79}\right)\)
\(\chi_{8061}(5,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{133}{158}\right)\)	\(e\left(\frac{54}{79}\right)\)	\(e\left(\frac{672}{1343}\right)\)	\(e\left(\frac{205}{1343}\right)\)	\(e\left(\frac{83}{158}\right)\)	\(e\left(\frac{919}{2686}\right)\)	\(e\left(\frac{295}{1343}\right)\)	\(e\left(\frac{66}{1343}\right)\)	\(e\left(\frac{2671}{2686}\right)\)	\(e\left(\frac{29}{79}\right)\)
\(\chi_{8061}(7,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{10}{79}\right)\)	\(e\left(\frac{20}{79}\right)\)	\(e\left(\frac{205}{1343}\right)\)	\(e\left(\frac{784}{1343}\right)\)	\(e\left(\frac{30}{79}\right)\)	\(e\left(\frac{375}{1343}\right)\)	\(e\left(\frac{80}{1343}\right)\)	\(e\left(\frac{200}{1343}\right)\)	\(e\left(\frac{954}{1343}\right)\)	\(e\left(\frac{40}{79}\right)\)
\(\chi_{8061}(8,\cdot)\)	8061.l	158	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{158}\right)\)	\(e\left(\frac{38}{79}\right)\)	\(e\left(\frac{83}{158}\right)\)	\(e\left(\frac{30}{79}\right)\)	\(e\left(\frac{35}{158}\right)\)	\(e\left(\frac{21}{79}\right)\)	\(e\left(\frac{69}{158}\right)\)	\(e\left(\frac{27}{79}\right)\)	\(e\left(\frac{19}{158}\right)\)	\(e\left(\frac{76}{79}\right)\)
\(\chi_{8061}(10,\cdot)\)	8061.n	2686	no	\(-1\)	\(1\)	\(e\left(\frac{7}{79}\right)\)	\(e\left(\frac{14}{79}\right)\)	\(e\left(\frac{919}{2686}\right)\)	\(e\left(\frac{375}{1343}\right)\)	\(e\left(\frac{21}{79}\right)\)	\(e\left(\frac{1157}{2686}\right)\)	\(e\left(\frac{981}{2686}\right)\)	\(e\left(\frac{219}{1343}\right)\)	\(e\left(\frac{494}{1343}\right)\)	\(e\left(\frac{28}{79}\right)\)
\(\chi_{8061}(11,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{23}{158}\right)\)	\(e\left(\frac{23}{79}\right)\)	\(e\left(\frac{295}{1343}\right)\)	\(e\left(\frac{80}{1343}\right)\)	\(e\left(\frac{69}{158}\right)\)	\(e\left(\frac{981}{2686}\right)\)	\(e\left(\frac{803}{1343}\right)\)	\(e\left(\frac{1336}{1343}\right)\)	\(e\left(\frac{551}{2686}\right)\)	\(e\left(\frac{46}{79}\right)\)
\(\chi_{8061}(13,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{9}{79}\right)\)	\(e\left(\frac{18}{79}\right)\)	\(e\left(\frac{66}{1343}\right)\)	\(e\left(\frac{200}{1343}\right)\)	\(e\left(\frac{27}{79}\right)\)	\(e\left(\frac{219}{1343}\right)\)	\(e\left(\frac{1336}{1343}\right)\)	\(e\left(\frac{654}{1343}\right)\)	\(e\left(\frac{353}{1343}\right)\)	\(e\left(\frac{36}{79}\right)\)
\(\chi_{8061}(14,\cdot)\)	8061.o	2686	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{158}\right)\)	\(e\left(\frac{59}{79}\right)\)	\(e\left(\frac{2671}{2686}\right)\)	\(e\left(\frac{954}{1343}\right)\)	\(e\left(\frac{19}{158}\right)\)	\(e\left(\frac{494}{1343}\right)\)	\(e\left(\frac{551}{2686}\right)\)	\(e\left(\frac{353}{1343}\right)\)	\(e\left(\frac{225}{2686}\right)\)	\(e\left(\frac{39}{79}\right)\)
\(\chi_{8061}(16,\cdot)\)	8061.i	79	no	\(1\)	\(1\)	\(e\left(\frac{78}{79}\right)\)	\(e\left(\frac{77}{79}\right)\)	\(e\left(\frac{29}{79}\right)\)	\(e\left(\frac{40}{79}\right)\)	\(e\left(\frac{76}{79}\right)\)	\(e\left(\frac{28}{79}\right)\)	\(e\left(\frac{46}{79}\right)\)	\(e\left(\frac{36}{79}\right)\)	\(e\left(\frac{39}{79}\right)\)	\(e\left(\frac{75}{79}\right)\)
\(\chi_{8061}(17,\cdot)\)	8061.o	2686	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{158}\right)\)	\(e\left(\frac{34}{79}\right)\)	\(e\left(\frac{2593}{2686}\right)\)	\(e\left(\frac{1080}{1343}\right)\)	\(e\left(\frac{23}{158}\right)\)	\(e\left(\frac{914}{1343}\right)\)	\(e\left(\frac{193}{2686}\right)\)	\(e\left(\frac{577}{1343}\right)\)	\(e\left(\frac{1395}{2686}\right)\)	\(e\left(\frac{68}{79}\right)\)
\(\chi_{8061}(19,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{77}{79}\right)\)	\(e\left(\frac{75}{79}\right)\)	\(e\left(\frac{38}{1343}\right)\)	\(e\left(\frac{807}{1343}\right)\)	\(e\left(\frac{73}{79}\right)\)	\(e\left(\frac{4}{1343}\right)\)	\(e\left(\frac{932}{1343}\right)\)	\(e\left(\frac{987}{1343}\right)\)	\(e\left(\frac{773}{1343}\right)\)	\(e\left(\frac{71}{79}\right)\)
\(\chi_{8061}(20,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{53}{158}\right)\)	\(e\left(\frac{53}{79}\right)\)	\(e\left(\frac{247}{1343}\right)\)	\(e\left(\frac{545}{1343}\right)\)	\(e\left(\frac{1}{158}\right)\)	\(e\left(\frac{1395}{2686}\right)\)	\(e\left(\frac{686}{1343}\right)\)	\(e\left(\frac{372}{1343}\right)\)	\(e\left(\frac{1991}{2686}\right)\)	\(e\left(\frac{27}{79}\right)\)
\(\chi_{8061}(22,\cdot)\)	8061.n	2686	no	\(-1\)	\(1\)	\(e\left(\frac{31}{79}\right)\)	\(e\left(\frac{62}{79}\right)\)	\(e\left(\frac{165}{2686}\right)\)	\(e\left(\frac{250}{1343}\right)\)	\(e\left(\frac{14}{79}\right)\)	\(e\left(\frac{1219}{2686}\right)\)	\(e\left(\frac{1997}{2686}\right)\)	\(e\left(\frac{146}{1343}\right)\)	\(e\left(\frac{777}{1343}\right)\)	\(e\left(\frac{45}{79}\right)\)
\(\chi_{8061}(23,\cdot)\)	8061.o	2686	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{158}\right)\)	\(e\left(\frac{14}{79}\right)\)	\(e\left(\frac{603}{2686}\right)\)	\(e\left(\frac{59}{1343}\right)\)	\(e\left(\frac{121}{158}\right)\)	\(e\left(\frac{1092}{1343}\right)\)	\(e\left(\frac{2561}{2686}\right)\)	\(e\left(\frac{851}{1343}\right)\)	\(e\left(\frac{1699}{2686}\right)\)	\(e\left(\frac{28}{79}\right)\)
\(\chi_{8061}(25,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{54}{79}\right)\)	\(e\left(\frac{29}{79}\right)\)	\(e\left(\frac{1}{1343}\right)\)	\(e\left(\frac{410}{1343}\right)\)	\(e\left(\frac{4}{79}\right)\)	\(e\left(\frac{919}{1343}\right)\)	\(e\left(\frac{590}{1343}\right)\)	\(e\left(\frac{132}{1343}\right)\)	\(e\left(\frac{1328}{1343}\right)\)	\(e\left(\frac{58}{79}\right)\)
\(\chi_{8061}(26,\cdot)\)	8061.o	2686	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{158}\right)\)	\(e\left(\frac{57}{79}\right)\)	\(e\left(\frac{2393}{2686}\right)\)	\(e\left(\frac{370}{1343}\right)\)	\(e\left(\frac{13}{158}\right)\)	\(e\left(\frac{338}{1343}\right)\)	\(e\left(\frac{377}{2686}\right)\)	\(e\left(\frac{807}{1343}\right)\)	\(e\left(\frac{1709}{2686}\right)\)	\(e\left(\frac{35}{79}\right)\)
\(\chi_{8061}(28,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{49}{79}\right)\)	\(e\left(\frac{19}{79}\right)\)	\(e\left(\frac{1123}{1343}\right)\)	\(e\left(\frac{1124}{1343}\right)\)	\(e\left(\frac{68}{79}\right)\)	\(e\left(\frac{613}{1343}\right)\)	\(e\left(\frac{471}{1343}\right)\)	\(e\left(\frac{506}{1343}\right)\)	\(e\left(\frac{614}{1343}\right)\)	\(e\left(\frac{38}{79}\right)\)
\(\chi_{8061}(29,\cdot)\)	8061.k	158	yes	\(1\)	\(1\)	\(e\left(\frac{141}{158}\right)\)	\(e\left(\frac{62}{79}\right)\)	\(e\left(\frac{49}{79}\right)\)	\(e\left(\frac{24}{79}\right)\)	\(e\left(\frac{107}{158}\right)\)	\(e\left(\frac{81}{158}\right)\)	\(e\left(\frac{75}{79}\right)\)	\(e\left(\frac{69}{79}\right)\)	\(e\left(\frac{31}{158}\right)\)	\(e\left(\frac{45}{79}\right)\)
\(\chi_{8061}(31,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{4}{79}\right)\)	\(e\left(\frac{8}{79}\right)\)	\(e\left(\frac{1030}{1343}\right)\)	\(e\left(\frac{598}{1343}\right)\)	\(e\left(\frac{12}{79}\right)\)	\(e\left(\frac{1098}{1343}\right)\)	\(e\left(\frac{664}{1343}\right)\)	\(e\left(\frac{317}{1343}\right)\)	\(e\left(\frac{666}{1343}\right)\)	\(e\left(\frac{16}{79}\right)\)
\(\chi_{8061}(32,\cdot)\)	8061.l	158	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{158}\right)\)	\(e\left(\frac{37}{79}\right)\)	\(e\left(\frac{33}{158}\right)\)	\(e\left(\frac{50}{79}\right)\)	\(e\left(\frac{111}{158}\right)\)	\(e\left(\frac{35}{79}\right)\)	\(e\left(\frac{115}{158}\right)\)	\(e\left(\frac{45}{79}\right)\)	\(e\left(\frac{137}{158}\right)\)	\(e\left(\frac{74}{79}\right)\)
\(\chi_{8061}(34,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{76}{79}\right)\)	\(e\left(\frac{73}{79}\right)\)	\(e\left(\frac{1084}{1343}\right)\)	\(e\left(\frac{1250}{1343}\right)\)	\(e\left(\frac{70}{79}\right)\)	\(e\left(\frac{1033}{1343}\right)\)	\(e\left(\frac{292}{1343}\right)\)	\(e\left(\frac{730}{1343}\right)\)	\(e\left(\frac{1199}{1343}\right)\)	\(e\left(\frac{67}{79}\right)\)
\(\chi_{8061}(35,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{153}{158}\right)\)	\(e\left(\frac{74}{79}\right)\)	\(e\left(\frac{877}{1343}\right)\)	\(e\left(\frac{989}{1343}\right)\)	\(e\left(\frac{143}{158}\right)\)	\(e\left(\frac{1669}{2686}\right)\)	\(e\left(\frac{375}{1343}\right)\)	\(e\left(\frac{266}{1343}\right)\)	\(e\left(\frac{1893}{2686}\right)\)	\(e\left(\frac{69}{79}\right)\)
\(\chi_{8061}(37,\cdot)\)	8061.n	2686	no	\(-1\)	\(1\)	\(e\left(\frac{44}{79}\right)\)	\(e\left(\frac{9}{79}\right)\)	\(e\left(\frac{777}{2686}\right)\)	\(e\left(\frac{811}{1343}\right)\)	\(e\left(\frac{53}{79}\right)\)	\(e\left(\frac{2273}{2686}\right)\)	\(e\left(\frac{467}{2686}\right)\)	\(e\left(\frac{248}{1343}\right)\)	\(e\left(\frac{216}{1343}\right)\)	\(e\left(\frac{18}{79}\right)\)
\(\chi_{8061}(38,\cdot)\)	8061.o	2686	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{158}\right)\)	\(e\left(\frac{35}{79}\right)\)	\(e\left(\frac{2337}{2686}\right)\)	\(e\left(\frac{977}{1343}\right)\)	\(e\left(\frac{105}{158}\right)\)	\(e\left(\frac{123}{1343}\right)\)	\(e\left(\frac{2255}{2686}\right)\)	\(e\left(\frac{1140}{1343}\right)\)	\(e\left(\frac{2549}{2686}\right)\)	\(e\left(\frac{70}{79}\right)\)
\(\chi_{8061}(40,\cdot)\)	8061.n	2686	no	\(-1\)	\(1\)	\(e\left(\frac{46}{79}\right)\)	\(e\left(\frac{13}{79}\right)\)	\(e\left(\frac{69}{2686}\right)\)	\(e\left(\frac{715}{1343}\right)\)	\(e\left(\frac{59}{79}\right)\)	\(e\left(\frac{1633}{2686}\right)\)	\(e\left(\frac{1763}{2686}\right)\)	\(e\left(\frac{525}{1343}\right)\)	\(e\left(\frac{154}{1343}\right)\)	\(e\left(\frac{26}{79}\right)\)
\(\chi_{8061}(41,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{69}{158}\right)\)	\(e\left(\frac{69}{79}\right)\)	\(e\left(\frac{16}{1343}\right)\)	\(e\left(\frac{1188}{1343}\right)\)	\(e\left(\frac{49}{158}\right)\)	\(e\left(\frac{1205}{2686}\right)\)	\(e\left(\frac{39}{1343}\right)\)	\(e\left(\frac{769}{1343}\right)\)	\(e\left(\frac{863}{2686}\right)\)	\(e\left(\frac{59}{79}\right)\)
\(\chi_{8061}(43,\cdot)\)	8061.n	2686	no	\(-1\)	\(1\)	\(e\left(\frac{77}{79}\right)\)	\(e\left(\frac{75}{79}\right)\)	\(e\left(\frac{2683}{2686}\right)\)	\(e\left(\frac{728}{1343}\right)\)	\(e\left(\frac{73}{79}\right)\)	\(e\left(\frac{2615}{2686}\right)\)	\(e\left(\frac{2259}{2686}\right)\)	\(e\left(\frac{1145}{1343}\right)\)	\(e\left(\frac{694}{1343}\right)\)	\(e\left(\frac{71}{79}\right)\)
\(\chi_{8061}(44,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{101}{158}\right)\)	\(e\left(\frac{22}{79}\right)\)	\(e\left(\frac{1213}{1343}\right)\)	\(e\left(\frac{420}{1343}\right)\)	\(e\left(\frac{145}{158}\right)\)	\(e\left(\frac{1457}{2686}\right)\)	\(e\left(\frac{1194}{1343}\right)\)	\(e\left(\frac{299}{1343}\right)\)	\(e\left(\frac{2557}{2686}\right)\)	\(e\left(\frac{44}{79}\right)\)
\(\chi_{8061}(46,\cdot)\)	8061.m	1343	no	\(1\)	\(1\)	\(e\left(\frac{66}{79}\right)\)	\(e\left(\frac{53}{79}\right)\)	\(e\left(\frac{89}{1343}\right)\)	\(e\left(\frac{229}{1343}\right)\)	\(e\left(\frac{40}{79}\right)\)	\(e\left(\frac{1211}{1343}\right)\)	\(e\left(\frac{133}{1343}\right)\)	\(e\left(\frac{1004}{1343}\right)\)	\(e\left(\frac{8}{1343}\right)\)	\(e\left(\frac{27}{79}\right)\)
\(\chi_{8061}(47,\cdot)\)	8061.p	2686	yes	\(1\)	\(1\)	\(e\left(\frac{19}{158}\right)\)	\(e\left(\frac{19}{79}\right)\)	\(e\left(\frac{728}{1343}\right)\)	\(e\left(\frac{334}{1343}\right)\)	\(e\left(\frac{57}{158}\right)\)	\(e\left(\frac{1779}{2686}\right)\)	\(e\left(\frac{1103}{1343}\right)\)	\(e\left(\frac{743}{1343}\right)\)	\(e\left(\frac{991}{2686}\right)\)	\(e\left(\frac{38}{79}\right)\)

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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.