LMFDB - Group of Dirichlet characters of modulus 1293

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1293)

gp:g = idealstar(,1293,2)

magma:G = FullDirichletGroup(1293);

Character group

Order	=	860	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{430}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1293}(863,\cdot)$, $\chi_{1293}(7,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 860 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1293}(1,\cdot)$	1293.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1293}(2,\cdot)$	1293.k	86	yes	$-1$	$1$	$e\left(\frac{5}{86}\right)$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{41}{86}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{15}{86}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{31}{86}\right)$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{49}{86}\right)$	$e\left(\frac{10}{43}\right)$
$\chi_{1293}(4,\cdot)$	1293.i	43	no	$1$	$1$	$e\left(\frac{5}{43}\right)$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{20}{43}\right)$
$\chi_{1293}(5,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{41}{86}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{219}{430}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{212}{215}\right)$	$e\left(\frac{411}{430}\right)$	$e\left(\frac{177}{215}\right)$	$e\left(\frac{117}{430}\right)$	$e\left(\frac{39}{43}\right)$
$\chi_{1293}(7,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{171}{215}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{66}{215}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{167}{430}\right)$	$e\left(\frac{221}{430}\right)$	$e\left(\frac{2}{43}\right)$
$\chi_{1293}(8,\cdot)$	1293.k	86	yes	$-1$	$1$	$e\left(\frac{15}{86}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{45}{86}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{61}{86}\right)$	$e\left(\frac{30}{43}\right)$
$\chi_{1293}(10,\cdot)$	1293.m	215	no	$1$	$1$	$e\left(\frac{23}{43}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{212}{215}\right)$	$e\left(\frac{66}{215}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{112}{215}\right)$	$e\left(\frac{68}{215}\right)$	$e\left(\frac{57}{215}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{6}{43}\right)$
$\chi_{1293}(11,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{31}{86}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{411}{430}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{68}{215}\right)$	$e\left(\frac{359}{430}\right)$	$e\left(\frac{73}{215}\right)$	$e\left(\frac{143}{430}\right)$	$e\left(\frac{19}{43}\right)$
$\chi_{1293}(13,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{177}{215}\right)$	$e\left(\frac{167}{430}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{57}{215}\right)$	$e\left(\frac{73}{215}\right)$	$e\left(\frac{369}{430}\right)$	$e\left(\frac{357}{430}\right)$	$e\left(\frac{33}{43}\right)$
$\chi_{1293}(14,\cdot)$	1293.o	430	yes	$1$	$1$	$e\left(\frac{49}{86}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{117}{430}\right)$	$e\left(\frac{221}{430}\right)$	$e\left(\frac{61}{86}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{143}{430}\right)$	$e\left(\frac{357}{430}\right)$	$e\left(\frac{18}{215}\right)$	$e\left(\frac{12}{43}\right)$
$\chi_{1293}(16,\cdot)$	1293.i	43	no	$1$	$1$	$e\left(\frac{10}{43}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{19}{43}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{12}{43}\right)$	$e\left(\frac{40}{43}\right)$
$\chi_{1293}(17,\cdot)$	1293.o	430	yes	$1$	$1$	$e\left(\frac{31}{86}\right)$	$e\left(\frac{31}{43}\right)$	$e\left(\frac{67}{430}\right)$	$e\left(\frac{31}{430}\right)$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{111}{215}\right)$	$e\left(\frac{273}{430}\right)$	$e\left(\frac{17}{430}\right)$	$e\left(\frac{93}{215}\right)$	$e\left(\frac{19}{43}\right)$
$\chi_{1293}(19,\cdot)$	1293.m	215	no	$1$	$1$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{84}{215}\right)$	$e\left(\frac{87}{215}\right)$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{89}{215}\right)$	$e\left(\frac{31}{215}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{92}{215}\right)$	$e\left(\frac{4}{43}\right)$
$\chi_{1293}(20,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{51}{86}\right)$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{199}{430}\right)$	$e\left(\frac{176}{215}\right)$	$e\left(\frac{67}{86}\right)$	$e\left(\frac{12}{215}\right)$	$e\left(\frac{291}{430}\right)$	$e\left(\frac{152}{215}\right)$	$e\left(\frac{177}{430}\right)$	$e\left(\frac{16}{43}\right)$
$\chi_{1293}(22,\cdot)$	1293.m	215	no	$1$	$1$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{93}{215}\right)$	$e\left(\frac{104}{215}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{183}{215}\right)$	$e\left(\frac{42}{215}\right)$	$e\left(\frac{168}{215}\right)$	$e\left(\frac{194}{215}\right)$	$e\left(\frac{29}{43}\right)$
$\chi_{1293}(23,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{25}{86}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{337}{430}\right)$	$e\left(\frac{163}{215}\right)$	$e\left(\frac{75}{86}\right)$	$e\left(\frac{16}{215}\right)$	$e\left(\frac{173}{430}\right)$	$e\left(\frac{131}{215}\right)$	$e\left(\frac{21}{430}\right)$	$e\left(\frac{7}{43}\right)$
$\chi_{1293}(25,\cdot)$	1293.m	215	no	$1$	$1$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{4}{215}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{37}{43}\right)$	$e\left(\frac{209}{215}\right)$	$e\left(\frac{196}{215}\right)$	$e\left(\frac{139}{215}\right)$	$e\left(\frac{117}{215}\right)$	$e\left(\frac{35}{43}\right)$
$\chi_{1293}(26,\cdot)$	1293.g	10	yes	$1$	$1$	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$
$\chi_{1293}(28,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{27}{43}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{161}{215}\right)$	$e\left(\frac{11}{430}\right)$	$e\left(\frac{38}{43}\right)$	$e\left(\frac{81}{215}\right)$	$e\left(\frac{149}{215}\right)$	$e\left(\frac{117}{430}\right)$	$e\left(\frac{281}{430}\right)$	$e\left(\frac{22}{43}\right)$
$\chi_{1293}(29,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{33}{86}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{321}{430}\right)$	$e\left(\frac{124}{215}\right)$	$e\left(\frac{13}{86}\right)$	$e\left(\frac{28}{215}\right)$	$e\left(\frac{249}{430}\right)$	$e\left(\frac{68}{215}\right)$	$e\left(\frac{413}{430}\right)$	$e\left(\frac{23}{43}\right)$
$\chi_{1293}(31,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{8}{43}\right)$	$e\left(\frac{16}{43}\right)$	$e\left(\frac{199}{215}\right)$	$e\left(\frac{59}{430}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{24}{215}\right)$	$e\left(\frac{76}{215}\right)$	$e\left(\frac{393}{430}\right)$	$e\left(\frac{139}{430}\right)$	$e\left(\frac{32}{43}\right)$
$\chi_{1293}(32,\cdot)$	1293.k	86	yes	$-1$	$1$	$e\left(\frac{25}{86}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{33}{86}\right)$	$e\left(\frac{24}{43}\right)$	$e\left(\frac{75}{86}\right)$	$e\left(\frac{29}{43}\right)$	$e\left(\frac{69}{86}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{73}{86}\right)$	$e\left(\frac{7}{43}\right)$
$\chi_{1293}(34,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{136}{215}\right)$	$e\left(\frac{251}{430}\right)$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{11}{215}\right)$	$e\left(\frac{214}{215}\right)$	$e\left(\frac{207}{430}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{29}{43}\right)$
$\chi_{1293}(35,\cdot)$	1293.o	430	yes	$1$	$1$	$e\left(\frac{85}{86}\right)$	$e\left(\frac{42}{43}\right)$	$e\left(\frac{131}{430}\right)$	$e\left(\frac{343}{430}\right)$	$e\left(\frac{83}{86}\right)$	$e\left(\frac{63}{215}\right)$	$e\left(\frac{399}{430}\right)$	$e\left(\frac{91}{430}\right)$	$e\left(\frac{169}{215}\right)$	$e\left(\frac{41}{43}\right)$
$\chi_{1293}(37,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{3}{43}\right)$	$e\left(\frac{6}{43}\right)$	$e\left(\frac{37}{215}\right)$	$e\left(\frac{307}{430}\right)$	$e\left(\frac{9}{43}\right)$	$e\left(\frac{52}{215}\right)$	$e\left(\frac{93}{215}\right)$	$e\left(\frac{99}{430}\right)$	$e\left(\frac{337}{430}\right)$	$e\left(\frac{12}{43}\right)$
$\chi_{1293}(38,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{7}{86}\right)$	$e\left(\frac{7}{43}\right)$	$e\left(\frac{373}{430}\right)$	$e\left(\frac{197}{215}\right)$	$e\left(\frac{21}{86}\right)$	$e\left(\frac{204}{215}\right)$	$e\left(\frac{217}{430}\right)$	$e\left(\frac{4}{215}\right)$	$e\left(\frac{429}{430}\right)$	$e\left(\frac{14}{43}\right)$
$\chi_{1293}(40,\cdot)$	1293.m	215	no	$1$	$1$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{13}{43}\right)$	$e\left(\frac{202}{215}\right)$	$e\left(\frac{71}{215}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{8}{215}\right)$	$e\left(\frac{32}{215}\right)$	$e\left(\frac{211}{215}\right)$	$e\left(\frac{26}{43}\right)$
$\chi_{1293}(41,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{63}{86}\right)$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{3}{430}\right)$	$e\left(\frac{182}{215}\right)$	$e\left(\frac{17}{86}\right)$	$e\left(\frac{159}{215}\right)$	$e\left(\frac{147}{430}\right)$	$e\left(\frac{79}{215}\right)$	$e\left(\frac{249}{430}\right)$	$e\left(\frac{40}{43}\right)$
$\chi_{1293}(43,\cdot)$	1293.n	430	no	$-1$	$1$	$e\left(\frac{20}{43}\right)$	$e\left(\frac{40}{43}\right)$	$e\left(\frac{3}{215}\right)$	$e\left(\frac{83}{430}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{103}{215}\right)$	$e\left(\frac{147}{215}\right)$	$e\left(\frac{101}{430}\right)$	$e\left(\frac{283}{430}\right)$	$e\left(\frac{37}{43}\right)$
$\chi_{1293}(44,\cdot)$	1293.p	430	yes	$-1$	$1$	$e\left(\frac{41}{86}\right)$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{391}{430}\right)$	$e\left(\frac{214}{215}\right)$	$e\left(\frac{37}{86}\right)$	$e\left(\frac{83}{215}\right)$	$e\left(\frac{239}{430}\right)$	$e\left(\frac{48}{215}\right)$	$e\left(\frac{203}{430}\right)$	$e\left(\frac{39}{43}\right)$
$\chi_{1293}(46,\cdot)$	1293.m	215	no	$1$	$1$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{56}{215}\right)$	$e\left(\frac{58}{215}\right)$	$e\left(\frac{2}{43}\right)$	$e\left(\frac{131}{215}\right)$	$e\left(\frac{164}{215}\right)$	$e\left(\frac{11}{215}\right)$	$e\left(\frac{133}{215}\right)$	$e\left(\frac{17}{43}\right)$
$\chi_{1293}(47,\cdot)$	1293.l	86	yes	$1$	$1$	$e\left(\frac{57}{86}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{3}{86}\right)$	$e\left(\frac{63}{86}\right)$	$e\left(\frac{85}{86}\right)$	$e\left(\frac{30}{43}\right)$	$e\left(\frac{61}{86}\right)$	$e\left(\frac{29}{86}\right)$	$e\left(\frac{17}{43}\right)$	$e\left(\frac{28}{43}\right)$

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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	$1293$
Structure	\(C_{2}\times C_{430}\)
Order	$860$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1293}(1,\cdot)\)	1293.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1293}(2,\cdot)\)	1293.k	86	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{86}\right)\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{41}{86}\right)\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{15}{86}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{31}{86}\right)\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{49}{86}\right)\)	\(e\left(\frac{10}{43}\right)\)
\(\chi_{1293}(4,\cdot)\)	1293.i	43	no	\(1\)	\(1\)	\(e\left(\frac{5}{43}\right)\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{20}{43}\right)\)
\(\chi_{1293}(5,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{86}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{219}{430}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{212}{215}\right)\)	\(e\left(\frac{411}{430}\right)\)	\(e\left(\frac{177}{215}\right)\)	\(e\left(\frac{117}{430}\right)\)	\(e\left(\frac{39}{43}\right)\)
\(\chi_{1293}(7,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{22}{43}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{171}{215}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{66}{215}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{167}{430}\right)\)	\(e\left(\frac{221}{430}\right)\)	\(e\left(\frac{2}{43}\right)\)
\(\chi_{1293}(8,\cdot)\)	1293.k	86	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{86}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{45}{86}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{61}{86}\right)\)	\(e\left(\frac{30}{43}\right)\)
\(\chi_{1293}(10,\cdot)\)	1293.m	215	no	\(1\)	\(1\)	\(e\left(\frac{23}{43}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{212}{215}\right)\)	\(e\left(\frac{66}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{112}{215}\right)\)	\(e\left(\frac{68}{215}\right)\)	\(e\left(\frac{57}{215}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{6}{43}\right)\)
\(\chi_{1293}(11,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{86}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{411}{430}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{68}{215}\right)\)	\(e\left(\frac{359}{430}\right)\)	\(e\left(\frac{73}{215}\right)\)	\(e\left(\frac{143}{430}\right)\)	\(e\left(\frac{19}{43}\right)\)
\(\chi_{1293}(13,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{177}{215}\right)\)	\(e\left(\frac{167}{430}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{57}{215}\right)\)	\(e\left(\frac{73}{215}\right)\)	\(e\left(\frac{369}{430}\right)\)	\(e\left(\frac{357}{430}\right)\)	\(e\left(\frac{33}{43}\right)\)
\(\chi_{1293}(14,\cdot)\)	1293.o	430	yes	\(1\)	\(1\)	\(e\left(\frac{49}{86}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{117}{430}\right)\)	\(e\left(\frac{221}{430}\right)\)	\(e\left(\frac{61}{86}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{143}{430}\right)\)	\(e\left(\frac{357}{430}\right)\)	\(e\left(\frac{18}{215}\right)\)	\(e\left(\frac{12}{43}\right)\)
\(\chi_{1293}(16,\cdot)\)	1293.i	43	no	\(1\)	\(1\)	\(e\left(\frac{10}{43}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{19}{43}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{12}{43}\right)\)	\(e\left(\frac{40}{43}\right)\)
\(\chi_{1293}(17,\cdot)\)	1293.o	430	yes	\(1\)	\(1\)	\(e\left(\frac{31}{86}\right)\)	\(e\left(\frac{31}{43}\right)\)	\(e\left(\frac{67}{430}\right)\)	\(e\left(\frac{31}{430}\right)\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{111}{215}\right)\)	\(e\left(\frac{273}{430}\right)\)	\(e\left(\frac{17}{430}\right)\)	\(e\left(\frac{93}{215}\right)\)	\(e\left(\frac{19}{43}\right)\)
\(\chi_{1293}(19,\cdot)\)	1293.m	215	no	\(1\)	\(1\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{84}{215}\right)\)	\(e\left(\frac{87}{215}\right)\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{89}{215}\right)\)	\(e\left(\frac{31}{215}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{92}{215}\right)\)	\(e\left(\frac{4}{43}\right)\)
\(\chi_{1293}(20,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{86}\right)\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{199}{430}\right)\)	\(e\left(\frac{176}{215}\right)\)	\(e\left(\frac{67}{86}\right)\)	\(e\left(\frac{12}{215}\right)\)	\(e\left(\frac{291}{430}\right)\)	\(e\left(\frac{152}{215}\right)\)	\(e\left(\frac{177}{430}\right)\)	\(e\left(\frac{16}{43}\right)\)
\(\chi_{1293}(22,\cdot)\)	1293.m	215	no	\(1\)	\(1\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{93}{215}\right)\)	\(e\left(\frac{104}{215}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{183}{215}\right)\)	\(e\left(\frac{42}{215}\right)\)	\(e\left(\frac{168}{215}\right)\)	\(e\left(\frac{194}{215}\right)\)	\(e\left(\frac{29}{43}\right)\)
\(\chi_{1293}(23,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{86}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{337}{430}\right)\)	\(e\left(\frac{163}{215}\right)\)	\(e\left(\frac{75}{86}\right)\)	\(e\left(\frac{16}{215}\right)\)	\(e\left(\frac{173}{430}\right)\)	\(e\left(\frac{131}{215}\right)\)	\(e\left(\frac{21}{430}\right)\)	\(e\left(\frac{7}{43}\right)\)
\(\chi_{1293}(25,\cdot)\)	1293.m	215	no	\(1\)	\(1\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{39}{43}\right)\)	\(e\left(\frac{4}{215}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{37}{43}\right)\)	\(e\left(\frac{209}{215}\right)\)	\(e\left(\frac{196}{215}\right)\)	\(e\left(\frac{139}{215}\right)\)	\(e\left(\frac{117}{215}\right)\)	\(e\left(\frac{35}{43}\right)\)
\(\chi_{1293}(26,\cdot)\)	1293.g	10	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)
\(\chi_{1293}(28,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{27}{43}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{161}{215}\right)\)	\(e\left(\frac{11}{430}\right)\)	\(e\left(\frac{38}{43}\right)\)	\(e\left(\frac{81}{215}\right)\)	\(e\left(\frac{149}{215}\right)\)	\(e\left(\frac{117}{430}\right)\)	\(e\left(\frac{281}{430}\right)\)	\(e\left(\frac{22}{43}\right)\)
\(\chi_{1293}(29,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{86}\right)\)	\(e\left(\frac{33}{43}\right)\)	\(e\left(\frac{321}{430}\right)\)	\(e\left(\frac{124}{215}\right)\)	\(e\left(\frac{13}{86}\right)\)	\(e\left(\frac{28}{215}\right)\)	\(e\left(\frac{249}{430}\right)\)	\(e\left(\frac{68}{215}\right)\)	\(e\left(\frac{413}{430}\right)\)	\(e\left(\frac{23}{43}\right)\)
\(\chi_{1293}(31,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{8}{43}\right)\)	\(e\left(\frac{16}{43}\right)\)	\(e\left(\frac{199}{215}\right)\)	\(e\left(\frac{59}{430}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{24}{215}\right)\)	\(e\left(\frac{76}{215}\right)\)	\(e\left(\frac{393}{430}\right)\)	\(e\left(\frac{139}{430}\right)\)	\(e\left(\frac{32}{43}\right)\)
\(\chi_{1293}(32,\cdot)\)	1293.k	86	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{86}\right)\)	\(e\left(\frac{25}{43}\right)\)	\(e\left(\frac{33}{86}\right)\)	\(e\left(\frac{24}{43}\right)\)	\(e\left(\frac{75}{86}\right)\)	\(e\left(\frac{29}{43}\right)\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{73}{86}\right)\)	\(e\left(\frac{7}{43}\right)\)
\(\chi_{1293}(34,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{136}{215}\right)\)	\(e\left(\frac{251}{430}\right)\)	\(e\left(\frac{11}{43}\right)\)	\(e\left(\frac{11}{215}\right)\)	\(e\left(\frac{214}{215}\right)\)	\(e\left(\frac{207}{430}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{29}{43}\right)\)
\(\chi_{1293}(35,\cdot)\)	1293.o	430	yes	\(1\)	\(1\)	\(e\left(\frac{85}{86}\right)\)	\(e\left(\frac{42}{43}\right)\)	\(e\left(\frac{131}{430}\right)\)	\(e\left(\frac{343}{430}\right)\)	\(e\left(\frac{83}{86}\right)\)	\(e\left(\frac{63}{215}\right)\)	\(e\left(\frac{399}{430}\right)\)	\(e\left(\frac{91}{430}\right)\)	\(e\left(\frac{169}{215}\right)\)	\(e\left(\frac{41}{43}\right)\)
\(\chi_{1293}(37,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{3}{43}\right)\)	\(e\left(\frac{6}{43}\right)\)	\(e\left(\frac{37}{215}\right)\)	\(e\left(\frac{307}{430}\right)\)	\(e\left(\frac{9}{43}\right)\)	\(e\left(\frac{52}{215}\right)\)	\(e\left(\frac{93}{215}\right)\)	\(e\left(\frac{99}{430}\right)\)	\(e\left(\frac{337}{430}\right)\)	\(e\left(\frac{12}{43}\right)\)
\(\chi_{1293}(38,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{86}\right)\)	\(e\left(\frac{7}{43}\right)\)	\(e\left(\frac{373}{430}\right)\)	\(e\left(\frac{197}{215}\right)\)	\(e\left(\frac{21}{86}\right)\)	\(e\left(\frac{204}{215}\right)\)	\(e\left(\frac{217}{430}\right)\)	\(e\left(\frac{4}{215}\right)\)	\(e\left(\frac{429}{430}\right)\)	\(e\left(\frac{14}{43}\right)\)
\(\chi_{1293}(40,\cdot)\)	1293.m	215	no	\(1\)	\(1\)	\(e\left(\frac{28}{43}\right)\)	\(e\left(\frac{13}{43}\right)\)	\(e\left(\frac{202}{215}\right)\)	\(e\left(\frac{71}{215}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{8}{215}\right)\)	\(e\left(\frac{32}{215}\right)\)	\(e\left(\frac{211}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)
\(\chi_{1293}(41,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{86}\right)\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{3}{430}\right)\)	\(e\left(\frac{182}{215}\right)\)	\(e\left(\frac{17}{86}\right)\)	\(e\left(\frac{159}{215}\right)\)	\(e\left(\frac{147}{430}\right)\)	\(e\left(\frac{79}{215}\right)\)	\(e\left(\frac{249}{430}\right)\)	\(e\left(\frac{40}{43}\right)\)
\(\chi_{1293}(43,\cdot)\)	1293.n	430	no	\(-1\)	\(1\)	\(e\left(\frac{20}{43}\right)\)	\(e\left(\frac{40}{43}\right)\)	\(e\left(\frac{3}{215}\right)\)	\(e\left(\frac{83}{430}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{103}{215}\right)\)	\(e\left(\frac{147}{215}\right)\)	\(e\left(\frac{101}{430}\right)\)	\(e\left(\frac{283}{430}\right)\)	\(e\left(\frac{37}{43}\right)\)
\(\chi_{1293}(44,\cdot)\)	1293.p	430	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{86}\right)\)	\(e\left(\frac{41}{43}\right)\)	\(e\left(\frac{391}{430}\right)\)	\(e\left(\frac{214}{215}\right)\)	\(e\left(\frac{37}{86}\right)\)	\(e\left(\frac{83}{215}\right)\)	\(e\left(\frac{239}{430}\right)\)	\(e\left(\frac{48}{215}\right)\)	\(e\left(\frac{203}{430}\right)\)	\(e\left(\frac{39}{43}\right)\)
\(\chi_{1293}(46,\cdot)\)	1293.m	215	no	\(1\)	\(1\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{56}{215}\right)\)	\(e\left(\frac{58}{215}\right)\)	\(e\left(\frac{2}{43}\right)\)	\(e\left(\frac{131}{215}\right)\)	\(e\left(\frac{164}{215}\right)\)	\(e\left(\frac{11}{215}\right)\)	\(e\left(\frac{133}{215}\right)\)	\(e\left(\frac{17}{43}\right)\)
\(\chi_{1293}(47,\cdot)\)	1293.l	86	yes	\(1\)	\(1\)	\(e\left(\frac{57}{86}\right)\)	\(e\left(\frac{14}{43}\right)\)	\(e\left(\frac{3}{86}\right)\)	\(e\left(\frac{63}{86}\right)\)	\(e\left(\frac{85}{86}\right)\)	\(e\left(\frac{30}{43}\right)\)	\(e\left(\frac{61}{86}\right)\)	\(e\left(\frac{29}{86}\right)\)	\(e\left(\frac{17}{43}\right)\)	\(e\left(\frac{28}{43}\right)\)

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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.