LMFDB - Group of Dirichlet characters of modulus 138917

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(138917)

gp:g = idealstar(,138917,2)

magma:G = FullDirichletGroup(138917);

Character group

Order	=	138916	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{138916}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{138917}(2,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 138916 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{138917}(1,\cdot)$	138917.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{138917}(2,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{1}{138916}\right)$	$e\left(\frac{132095}{138916}\right)$	$e\left(\frac{1}{69458}\right)$	$e\left(\frac{113707}{138916}\right)$	$e\left(\frac{33024}{34729}\right)$	$e\left(\frac{21739}{34729}\right)$	$e\left(\frac{3}{138916}\right)$	$e\left(\frac{62637}{69458}\right)$	$e\left(\frac{28427}{34729}\right)$	$e\left(\frac{7287}{69458}\right)$
$\chi_{138917}(3,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{132095}{138916}\right)$	$e\left(\frac{128097}{138916}\right)$	$e\left(\frac{62637}{69458}\right)$	$e\left(\frac{111497}{138916}\right)$	$e\left(\frac{30319}{34729}\right)$	$e\left(\frac{11111}{34729}\right)$	$e\left(\frac{118453}{138916}\right)$	$e\left(\frac{58639}{69458}\right)$	$e\left(\frac{26169}{34729}\right)$	$e\left(\frac{27301}{69458}\right)$
$\chi_{138917}(4,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{1}{69458}\right)$	$e\left(\frac{62637}{69458}\right)$	$e\left(\frac{1}{34729}\right)$	$e\left(\frac{44249}{69458}\right)$	$e\left(\frac{31319}{34729}\right)$	$e\left(\frac{8749}{34729}\right)$	$e\left(\frac{3}{69458}\right)$	$e\left(\frac{27908}{34729}\right)$	$e\left(\frac{22125}{34729}\right)$	$e\left(\frac{7287}{34729}\right)$
$\chi_{138917}(5,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{113707}{138916}\right)$	$e\left(\frac{111497}{138916}\right)$	$e\left(\frac{44249}{69458}\right)$	$e\left(\frac{91897}{138916}\right)$	$e\left(\frac{21572}{34729}\right)$	$e\left(\frac{5169}{34729}\right)$	$e\left(\frac{63289}{138916}\right)$	$e\left(\frac{42039}{69458}\right)$	$e\left(\frac{16672}{34729}\right)$	$e\left(\frac{18427}{69458}\right)$
$\chi_{138917}(6,\cdot)$	138917.d	34729	yes	$1$	$1$	$e\left(\frac{33024}{34729}\right)$	$e\left(\frac{30319}{34729}\right)$	$e\left(\frac{31319}{34729}\right)$	$e\left(\frac{21572}{34729}\right)$	$e\left(\frac{28614}{34729}\right)$	$e\left(\frac{32850}{34729}\right)$	$e\left(\frac{29614}{34729}\right)$	$e\left(\frac{25909}{34729}\right)$	$e\left(\frac{19867}{34729}\right)$	$e\left(\frac{17294}{34729}\right)$
$\chi_{138917}(7,\cdot)$	138917.d	34729	yes	$1$	$1$	$e\left(\frac{21739}{34729}\right)$	$e\left(\frac{11111}{34729}\right)$	$e\left(\frac{8749}{34729}\right)$	$e\left(\frac{5169}{34729}\right)$	$e\left(\frac{32850}{34729}\right)$	$e\left(\frac{2285}{34729}\right)$	$e\left(\frac{30488}{34729}\right)$	$e\left(\frac{22222}{34729}\right)$	$e\left(\frac{26908}{34729}\right)$	$e\left(\frac{26248}{34729}\right)$
$\chi_{138917}(8,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{3}{138916}\right)$	$e\left(\frac{118453}{138916}\right)$	$e\left(\frac{3}{69458}\right)$	$e\left(\frac{63289}{138916}\right)$	$e\left(\frac{29614}{34729}\right)$	$e\left(\frac{30488}{34729}\right)$	$e\left(\frac{9}{138916}\right)$	$e\left(\frac{48995}{69458}\right)$	$e\left(\frac{15823}{34729}\right)$	$e\left(\frac{21861}{69458}\right)$
$\chi_{138917}(9,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{62637}{69458}\right)$	$e\left(\frac{58639}{69458}\right)$	$e\left(\frac{27908}{34729}\right)$	$e\left(\frac{42039}{69458}\right)$	$e\left(\frac{25909}{34729}\right)$	$e\left(\frac{22222}{34729}\right)$	$e\left(\frac{48995}{69458}\right)$	$e\left(\frac{23910}{34729}\right)$	$e\left(\frac{17609}{34729}\right)$	$e\left(\frac{27301}{34729}\right)$
$\chi_{138917}(10,\cdot)$	138917.d	34729	yes	$1$	$1$	$e\left(\frac{28427}{34729}\right)$	$e\left(\frac{26169}{34729}\right)$	$e\left(\frac{22125}{34729}\right)$	$e\left(\frac{16672}{34729}\right)$	$e\left(\frac{19867}{34729}\right)$	$e\left(\frac{26908}{34729}\right)$	$e\left(\frac{15823}{34729}\right)$	$e\left(\frac{17609}{34729}\right)$	$e\left(\frac{10370}{34729}\right)$	$e\left(\frac{12857}{34729}\right)$
$\chi_{138917}(11,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{7287}{69458}\right)$	$e\left(\frac{27301}{69458}\right)$	$e\left(\frac{7287}{34729}\right)$	$e\left(\frac{18427}{69458}\right)$	$e\left(\frac{17294}{34729}\right)$	$e\left(\frac{26248}{34729}\right)$	$e\left(\frac{21861}{69458}\right)$	$e\left(\frac{27301}{34729}\right)$	$e\left(\frac{12857}{34729}\right)$	$e\left(\frac{34457}{34729}\right)$
$\chi_{138917}(12,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{132097}{138916}\right)$	$e\left(\frac{114455}{138916}\right)$	$e\left(\frac{62639}{69458}\right)$	$e\left(\frac{61079}{138916}\right)$	$e\left(\frac{26909}{34729}\right)$	$e\left(\frac{19860}{34729}\right)$	$e\left(\frac{118459}{138916}\right)$	$e\left(\frac{44997}{69458}\right)$	$e\left(\frac{13565}{34729}\right)$	$e\left(\frac{41875}{69458}\right)$
$\chi_{138917}(13,\cdot)$	138917.d	34729	yes	$1$	$1$	$e\left(\frac{25491}{34729}\right)$	$e\left(\frac{13992}{34729}\right)$	$e\left(\frac{16253}{34729}\right)$	$e\left(\frac{22797}{34729}\right)$	$e\left(\frac{4754}{34729}\right)$	$e\left(\frac{16971}{34729}\right)$	$e\left(\frac{7015}{34729}\right)$	$e\left(\frac{27984}{34729}\right)$	$e\left(\frac{13559}{34729}\right)$	$e\left(\frac{9721}{34729}\right)$
$\chi_{138917}(14,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{86957}{138916}\right)$	$e\left(\frac{37623}{138916}\right)$	$e\left(\frac{17499}{69458}\right)$	$e\left(\frac{134383}{138916}\right)$	$e\left(\frac{31145}{34729}\right)$	$e\left(\frac{24024}{34729}\right)$	$e\left(\frac{121955}{138916}\right)$	$e\left(\frac{37623}{69458}\right)$	$e\left(\frac{20606}{34729}\right)$	$e\left(\frac{59783}{69458}\right)$
$\chi_{138917}(15,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{53443}{69458}\right)$	$e\left(\frac{50339}{69458}\right)$	$e\left(\frac{18714}{34729}\right)$	$e\left(\frac{32239}{69458}\right)$	$e\left(\frac{17162}{34729}\right)$	$e\left(\frac{16280}{34729}\right)$	$e\left(\frac{21413}{69458}\right)$	$e\left(\frac{15610}{34729}\right)$	$e\left(\frac{8112}{34729}\right)$	$e\left(\frac{22864}{34729}\right)$
$\chi_{138917}(16,\cdot)$	138917.d	34729	yes	$1$	$1$	$e\left(\frac{1}{34729}\right)$	$e\left(\frac{27908}{34729}\right)$	$e\left(\frac{2}{34729}\right)$	$e\left(\frac{9520}{34729}\right)$	$e\left(\frac{27909}{34729}\right)$	$e\left(\frac{17498}{34729}\right)$	$e\left(\frac{3}{34729}\right)$	$e\left(\frac{21087}{34729}\right)$	$e\left(\frac{9521}{34729}\right)$	$e\left(\frac{14574}{34729}\right)$
$\chi_{138917}(17,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{69265}{138916}\right)$	$e\left(\frac{135667}{138916}\right)$	$e\left(\frac{69265}{69458}\right)$	$e\left(\frac{72735}{138916}\right)$	$e\left(\frac{16504}{34729}\right)$	$e\left(\frac{6582}{34729}\right)$	$e\left(\frac{68879}{138916}\right)$	$e\left(\frac{66209}{69458}\right)$	$e\left(\frac{771}{34729}\right)$	$e\left(\frac{52227}{69458}\right)$
$\chi_{138917}(18,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{125275}{138916}\right)$	$e\left(\frac{110457}{138916}\right)$	$e\left(\frac{55817}{69458}\right)$	$e\left(\frac{58869}{138916}\right)$	$e\left(\frac{24204}{34729}\right)$	$e\left(\frac{9232}{34729}\right)$	$e\left(\frac{97993}{138916}\right)$	$e\left(\frac{40999}{69458}\right)$	$e\left(\frac{11307}{34729}\right)$	$e\left(\frac{61889}{69458}\right)$
$\chi_{138917}(19,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{65931}{138916}\right)$	$e\left(\frac{94657}{138916}\right)$	$e\left(\frac{65931}{69458}\right)$	$e\left(\frac{75361}{138916}\right)$	$e\left(\frac{5418}{34729}\right)$	$e\left(\frac{8179}{34729}\right)$	$e\left(\frac{58877}{138916}\right)$	$e\left(\frac{25199}{69458}\right)$	$e\left(\frac{594}{34729}\right)$	$e\left(\frac{67669}{69458}\right)$
$\chi_{138917}(20,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{113709}{138916}\right)$	$e\left(\frac{97855}{138916}\right)$	$e\left(\frac{44251}{69458}\right)$	$e\left(\frac{41479}{138916}\right)$	$e\left(\frac{18162}{34729}\right)$	$e\left(\frac{13918}{34729}\right)$	$e\left(\frac{63295}{138916}\right)$	$e\left(\frac{28397}{69458}\right)$	$e\left(\frac{4068}{34729}\right)$	$e\left(\frac{33001}{69458}\right)$
$\chi_{138917}(21,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{80135}{138916}\right)$	$e\left(\frac{33625}{138916}\right)$	$e\left(\frac{10677}{69458}\right)$	$e\left(\frac{132173}{138916}\right)$	$e\left(\frac{28440}{34729}\right)$	$e\left(\frac{13396}{34729}\right)$	$e\left(\frac{101489}{138916}\right)$	$e\left(\frac{33625}{69458}\right)$	$e\left(\frac{18348}{34729}\right)$	$e\left(\frac{10339}{69458}\right)$
$\chi_{138917}(22,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{14575}{138916}\right)$	$e\left(\frac{47781}{138916}\right)$	$e\left(\frac{14575}{69458}\right)$	$e\left(\frac{11645}{138916}\right)$	$e\left(\frac{15589}{34729}\right)$	$e\left(\frac{13258}{34729}\right)$	$e\left(\frac{43725}{138916}\right)$	$e\left(\frac{47781}{69458}\right)$	$e\left(\frac{6555}{34729}\right)$	$e\left(\frac{6743}{69458}\right)$
$\chi_{138917}(23,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{17341}{138916}\right)$	$e\left(\frac{73471}{138916}\right)$	$e\left(\frac{17341}{69458}\right)$	$e\left(\frac{19383}{138916}\right)$	$e\left(\frac{22703}{34729}\right)$	$e\left(\frac{27433}{34729}\right)$	$e\left(\frac{52023}{138916}\right)$	$e\left(\frac{4013}{69458}\right)$	$e\left(\frac{9181}{34729}\right)$	$e\left(\frac{19765}{69458}\right)$
$\chi_{138917}(24,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{66049}{69458}\right)$	$e\left(\frac{53817}{69458}\right)$	$e\left(\frac{31320}{34729}\right)$	$e\left(\frac{17935}{69458}\right)$	$e\left(\frac{25204}{34729}\right)$	$e\left(\frac{6870}{34729}\right)$	$e\left(\frac{59231}{69458}\right)$	$e\left(\frac{19088}{34729}\right)$	$e\left(\frac{7263}{34729}\right)$	$e\left(\frac{24581}{34729}\right)$
$\chi_{138917}(25,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{44249}{69458}\right)$	$e\left(\frac{42039}{69458}\right)$	$e\left(\frac{9520}{34729}\right)$	$e\left(\frac{22439}{69458}\right)$	$e\left(\frac{8415}{34729}\right)$	$e\left(\frac{10338}{34729}\right)$	$e\left(\frac{63289}{69458}\right)$	$e\left(\frac{7310}{34729}\right)$	$e\left(\frac{33344}{34729}\right)$	$e\left(\frac{18427}{34729}\right)$
$\chi_{138917}(26,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{101965}{138916}\right)$	$e\left(\frac{49147}{138916}\right)$	$e\left(\frac{32507}{69458}\right)$	$e\left(\frac{65979}{138916}\right)$	$e\left(\frac{3049}{34729}\right)$	$e\left(\frac{3981}{34729}\right)$	$e\left(\frac{28063}{138916}\right)$	$e\left(\frac{49147}{69458}\right)$	$e\left(\frac{7257}{34729}\right)$	$e\left(\frac{26729}{69458}\right)$
$\chi_{138917}(27,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{118453}{138916}\right)$	$e\left(\frac{106459}{138916}\right)$	$e\left(\frac{48995}{69458}\right)$	$e\left(\frac{56659}{138916}\right)$	$e\left(\frac{21499}{34729}\right)$	$e\left(\frac{33333}{34729}\right)$	$e\left(\frac{77527}{138916}\right)$	$e\left(\frac{37001}{69458}\right)$	$e\left(\frac{9049}{34729}\right)$	$e\left(\frac{12445}{69458}\right)$
$\chi_{138917}(28,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{43479}{69458}\right)$	$e\left(\frac{15401}{69458}\right)$	$e\left(\frac{8750}{34729}\right)$	$e\left(\frac{54587}{69458}\right)$	$e\left(\frac{29440}{34729}\right)$	$e\left(\frac{11034}{34729}\right)$	$e\left(\frac{60979}{69458}\right)$	$e\left(\frac{15401}{34729}\right)$	$e\left(\frac{14304}{34729}\right)$	$e\left(\frac{33535}{34729}\right)$
$\chi_{138917}(29,\cdot)$	138917.e	69458	yes	$1$	$1$	$e\left(\frac{3483}{69458}\right)$	$e\left(\frac{66551}{69458}\right)$	$e\left(\frac{3483}{34729}\right)$	$e\left(\frac{61423}{69458}\right)$	$e\left(\frac{288}{34729}\right)$	$e\left(\frac{15434}{34729}\right)$	$e\left(\frac{10449}{69458}\right)$	$e\left(\frac{31822}{34729}\right)$	$e\left(\frac{32453}{34729}\right)$	$e\left(\frac{28451}{34729}\right)$
$\chi_{138917}(30,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{106887}{138916}\right)$	$e\left(\frac{93857}{138916}\right)$	$e\left(\frac{37429}{69458}\right)$	$e\left(\frac{39269}{138916}\right)$	$e\left(\frac{15457}{34729}\right)$	$e\left(\frac{3290}{34729}\right)$	$e\left(\frac{42829}{138916}\right)$	$e\left(\frac{24399}{69458}\right)$	$e\left(\frac{1810}{34729}\right)$	$e\left(\frac{53015}{69458}\right)$
$\chi_{138917}(31,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{62385}{138916}\right)$	$e\left(\frac{110539}{138916}\right)$	$e\left(\frac{62385}{69458}\right)$	$e\left(\frac{4571}{138916}\right)$	$e\left(\frac{8502}{34729}\right)$	$e\left(\frac{20065}{34729}\right)$	$e\left(\frac{48239}{138916}\right)$	$e\left(\frac{41081}{69458}\right)$	$e\left(\frac{16739}{34729}\right)$	$e\left(\frac{66343}{69458}\right)$
$\chi_{138917}(32,\cdot)$	138917.f	138916	yes	$-1$	$1$	$e\left(\frac{5}{138916}\right)$	$e\left(\frac{104811}{138916}\right)$	$e\left(\frac{5}{69458}\right)$	$e\left(\frac{12871}{138916}\right)$	$e\left(\frac{26204}{34729}\right)$	$e\left(\frac{4508}{34729}\right)$	$e\left(\frac{15}{138916}\right)$	$e\left(\frac{35353}{69458}\right)$	$e\left(\frac{3219}{34729}\right)$	$e\left(\frac{36435}{69458}\right)$

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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	$138917$
Structure	\(C_{138916}\)
Order	$138916$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{138917}(1,\cdot)\)	138917.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{138917}(2,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{138916}\right)\)	\(e\left(\frac{132095}{138916}\right)\)	\(e\left(\frac{1}{69458}\right)\)	\(e\left(\frac{113707}{138916}\right)\)	\(e\left(\frac{33024}{34729}\right)\)	\(e\left(\frac{21739}{34729}\right)\)	\(e\left(\frac{3}{138916}\right)\)	\(e\left(\frac{62637}{69458}\right)\)	\(e\left(\frac{28427}{34729}\right)\)	\(e\left(\frac{7287}{69458}\right)\)
\(\chi_{138917}(3,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{132095}{138916}\right)\)	\(e\left(\frac{128097}{138916}\right)\)	\(e\left(\frac{62637}{69458}\right)\)	\(e\left(\frac{111497}{138916}\right)\)	\(e\left(\frac{30319}{34729}\right)\)	\(e\left(\frac{11111}{34729}\right)\)	\(e\left(\frac{118453}{138916}\right)\)	\(e\left(\frac{58639}{69458}\right)\)	\(e\left(\frac{26169}{34729}\right)\)	\(e\left(\frac{27301}{69458}\right)\)
\(\chi_{138917}(4,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{1}{69458}\right)\)	\(e\left(\frac{62637}{69458}\right)\)	\(e\left(\frac{1}{34729}\right)\)	\(e\left(\frac{44249}{69458}\right)\)	\(e\left(\frac{31319}{34729}\right)\)	\(e\left(\frac{8749}{34729}\right)\)	\(e\left(\frac{3}{69458}\right)\)	\(e\left(\frac{27908}{34729}\right)\)	\(e\left(\frac{22125}{34729}\right)\)	\(e\left(\frac{7287}{34729}\right)\)
\(\chi_{138917}(5,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{113707}{138916}\right)\)	\(e\left(\frac{111497}{138916}\right)\)	\(e\left(\frac{44249}{69458}\right)\)	\(e\left(\frac{91897}{138916}\right)\)	\(e\left(\frac{21572}{34729}\right)\)	\(e\left(\frac{5169}{34729}\right)\)	\(e\left(\frac{63289}{138916}\right)\)	\(e\left(\frac{42039}{69458}\right)\)	\(e\left(\frac{16672}{34729}\right)\)	\(e\left(\frac{18427}{69458}\right)\)
\(\chi_{138917}(6,\cdot)\)	138917.d	34729	yes	\(1\)	\(1\)	\(e\left(\frac{33024}{34729}\right)\)	\(e\left(\frac{30319}{34729}\right)\)	\(e\left(\frac{31319}{34729}\right)\)	\(e\left(\frac{21572}{34729}\right)\)	\(e\left(\frac{28614}{34729}\right)\)	\(e\left(\frac{32850}{34729}\right)\)	\(e\left(\frac{29614}{34729}\right)\)	\(e\left(\frac{25909}{34729}\right)\)	\(e\left(\frac{19867}{34729}\right)\)	\(e\left(\frac{17294}{34729}\right)\)
\(\chi_{138917}(7,\cdot)\)	138917.d	34729	yes	\(1\)	\(1\)	\(e\left(\frac{21739}{34729}\right)\)	\(e\left(\frac{11111}{34729}\right)\)	\(e\left(\frac{8749}{34729}\right)\)	\(e\left(\frac{5169}{34729}\right)\)	\(e\left(\frac{32850}{34729}\right)\)	\(e\left(\frac{2285}{34729}\right)\)	\(e\left(\frac{30488}{34729}\right)\)	\(e\left(\frac{22222}{34729}\right)\)	\(e\left(\frac{26908}{34729}\right)\)	\(e\left(\frac{26248}{34729}\right)\)
\(\chi_{138917}(8,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{138916}\right)\)	\(e\left(\frac{118453}{138916}\right)\)	\(e\left(\frac{3}{69458}\right)\)	\(e\left(\frac{63289}{138916}\right)\)	\(e\left(\frac{29614}{34729}\right)\)	\(e\left(\frac{30488}{34729}\right)\)	\(e\left(\frac{9}{138916}\right)\)	\(e\left(\frac{48995}{69458}\right)\)	\(e\left(\frac{15823}{34729}\right)\)	\(e\left(\frac{21861}{69458}\right)\)
\(\chi_{138917}(9,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{62637}{69458}\right)\)	\(e\left(\frac{58639}{69458}\right)\)	\(e\left(\frac{27908}{34729}\right)\)	\(e\left(\frac{42039}{69458}\right)\)	\(e\left(\frac{25909}{34729}\right)\)	\(e\left(\frac{22222}{34729}\right)\)	\(e\left(\frac{48995}{69458}\right)\)	\(e\left(\frac{23910}{34729}\right)\)	\(e\left(\frac{17609}{34729}\right)\)	\(e\left(\frac{27301}{34729}\right)\)
\(\chi_{138917}(10,\cdot)\)	138917.d	34729	yes	\(1\)	\(1\)	\(e\left(\frac{28427}{34729}\right)\)	\(e\left(\frac{26169}{34729}\right)\)	\(e\left(\frac{22125}{34729}\right)\)	\(e\left(\frac{16672}{34729}\right)\)	\(e\left(\frac{19867}{34729}\right)\)	\(e\left(\frac{26908}{34729}\right)\)	\(e\left(\frac{15823}{34729}\right)\)	\(e\left(\frac{17609}{34729}\right)\)	\(e\left(\frac{10370}{34729}\right)\)	\(e\left(\frac{12857}{34729}\right)\)
\(\chi_{138917}(11,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{7287}{69458}\right)\)	\(e\left(\frac{27301}{69458}\right)\)	\(e\left(\frac{7287}{34729}\right)\)	\(e\left(\frac{18427}{69458}\right)\)	\(e\left(\frac{17294}{34729}\right)\)	\(e\left(\frac{26248}{34729}\right)\)	\(e\left(\frac{21861}{69458}\right)\)	\(e\left(\frac{27301}{34729}\right)\)	\(e\left(\frac{12857}{34729}\right)\)	\(e\left(\frac{34457}{34729}\right)\)
\(\chi_{138917}(12,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{132097}{138916}\right)\)	\(e\left(\frac{114455}{138916}\right)\)	\(e\left(\frac{62639}{69458}\right)\)	\(e\left(\frac{61079}{138916}\right)\)	\(e\left(\frac{26909}{34729}\right)\)	\(e\left(\frac{19860}{34729}\right)\)	\(e\left(\frac{118459}{138916}\right)\)	\(e\left(\frac{44997}{69458}\right)\)	\(e\left(\frac{13565}{34729}\right)\)	\(e\left(\frac{41875}{69458}\right)\)
\(\chi_{138917}(13,\cdot)\)	138917.d	34729	yes	\(1\)	\(1\)	\(e\left(\frac{25491}{34729}\right)\)	\(e\left(\frac{13992}{34729}\right)\)	\(e\left(\frac{16253}{34729}\right)\)	\(e\left(\frac{22797}{34729}\right)\)	\(e\left(\frac{4754}{34729}\right)\)	\(e\left(\frac{16971}{34729}\right)\)	\(e\left(\frac{7015}{34729}\right)\)	\(e\left(\frac{27984}{34729}\right)\)	\(e\left(\frac{13559}{34729}\right)\)	\(e\left(\frac{9721}{34729}\right)\)
\(\chi_{138917}(14,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{86957}{138916}\right)\)	\(e\left(\frac{37623}{138916}\right)\)	\(e\left(\frac{17499}{69458}\right)\)	\(e\left(\frac{134383}{138916}\right)\)	\(e\left(\frac{31145}{34729}\right)\)	\(e\left(\frac{24024}{34729}\right)\)	\(e\left(\frac{121955}{138916}\right)\)	\(e\left(\frac{37623}{69458}\right)\)	\(e\left(\frac{20606}{34729}\right)\)	\(e\left(\frac{59783}{69458}\right)\)
\(\chi_{138917}(15,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{53443}{69458}\right)\)	\(e\left(\frac{50339}{69458}\right)\)	\(e\left(\frac{18714}{34729}\right)\)	\(e\left(\frac{32239}{69458}\right)\)	\(e\left(\frac{17162}{34729}\right)\)	\(e\left(\frac{16280}{34729}\right)\)	\(e\left(\frac{21413}{69458}\right)\)	\(e\left(\frac{15610}{34729}\right)\)	\(e\left(\frac{8112}{34729}\right)\)	\(e\left(\frac{22864}{34729}\right)\)
\(\chi_{138917}(16,\cdot)\)	138917.d	34729	yes	\(1\)	\(1\)	\(e\left(\frac{1}{34729}\right)\)	\(e\left(\frac{27908}{34729}\right)\)	\(e\left(\frac{2}{34729}\right)\)	\(e\left(\frac{9520}{34729}\right)\)	\(e\left(\frac{27909}{34729}\right)\)	\(e\left(\frac{17498}{34729}\right)\)	\(e\left(\frac{3}{34729}\right)\)	\(e\left(\frac{21087}{34729}\right)\)	\(e\left(\frac{9521}{34729}\right)\)	\(e\left(\frac{14574}{34729}\right)\)
\(\chi_{138917}(17,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{69265}{138916}\right)\)	\(e\left(\frac{135667}{138916}\right)\)	\(e\left(\frac{69265}{69458}\right)\)	\(e\left(\frac{72735}{138916}\right)\)	\(e\left(\frac{16504}{34729}\right)\)	\(e\left(\frac{6582}{34729}\right)\)	\(e\left(\frac{68879}{138916}\right)\)	\(e\left(\frac{66209}{69458}\right)\)	\(e\left(\frac{771}{34729}\right)\)	\(e\left(\frac{52227}{69458}\right)\)
\(\chi_{138917}(18,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{125275}{138916}\right)\)	\(e\left(\frac{110457}{138916}\right)\)	\(e\left(\frac{55817}{69458}\right)\)	\(e\left(\frac{58869}{138916}\right)\)	\(e\left(\frac{24204}{34729}\right)\)	\(e\left(\frac{9232}{34729}\right)\)	\(e\left(\frac{97993}{138916}\right)\)	\(e\left(\frac{40999}{69458}\right)\)	\(e\left(\frac{11307}{34729}\right)\)	\(e\left(\frac{61889}{69458}\right)\)
\(\chi_{138917}(19,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{65931}{138916}\right)\)	\(e\left(\frac{94657}{138916}\right)\)	\(e\left(\frac{65931}{69458}\right)\)	\(e\left(\frac{75361}{138916}\right)\)	\(e\left(\frac{5418}{34729}\right)\)	\(e\left(\frac{8179}{34729}\right)\)	\(e\left(\frac{58877}{138916}\right)\)	\(e\left(\frac{25199}{69458}\right)\)	\(e\left(\frac{594}{34729}\right)\)	\(e\left(\frac{67669}{69458}\right)\)
\(\chi_{138917}(20,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{113709}{138916}\right)\)	\(e\left(\frac{97855}{138916}\right)\)	\(e\left(\frac{44251}{69458}\right)\)	\(e\left(\frac{41479}{138916}\right)\)	\(e\left(\frac{18162}{34729}\right)\)	\(e\left(\frac{13918}{34729}\right)\)	\(e\left(\frac{63295}{138916}\right)\)	\(e\left(\frac{28397}{69458}\right)\)	\(e\left(\frac{4068}{34729}\right)\)	\(e\left(\frac{33001}{69458}\right)\)
\(\chi_{138917}(21,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{80135}{138916}\right)\)	\(e\left(\frac{33625}{138916}\right)\)	\(e\left(\frac{10677}{69458}\right)\)	\(e\left(\frac{132173}{138916}\right)\)	\(e\left(\frac{28440}{34729}\right)\)	\(e\left(\frac{13396}{34729}\right)\)	\(e\left(\frac{101489}{138916}\right)\)	\(e\left(\frac{33625}{69458}\right)\)	\(e\left(\frac{18348}{34729}\right)\)	\(e\left(\frac{10339}{69458}\right)\)
\(\chi_{138917}(22,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{14575}{138916}\right)\)	\(e\left(\frac{47781}{138916}\right)\)	\(e\left(\frac{14575}{69458}\right)\)	\(e\left(\frac{11645}{138916}\right)\)	\(e\left(\frac{15589}{34729}\right)\)	\(e\left(\frac{13258}{34729}\right)\)	\(e\left(\frac{43725}{138916}\right)\)	\(e\left(\frac{47781}{69458}\right)\)	\(e\left(\frac{6555}{34729}\right)\)	\(e\left(\frac{6743}{69458}\right)\)
\(\chi_{138917}(23,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{17341}{138916}\right)\)	\(e\left(\frac{73471}{138916}\right)\)	\(e\left(\frac{17341}{69458}\right)\)	\(e\left(\frac{19383}{138916}\right)\)	\(e\left(\frac{22703}{34729}\right)\)	\(e\left(\frac{27433}{34729}\right)\)	\(e\left(\frac{52023}{138916}\right)\)	\(e\left(\frac{4013}{69458}\right)\)	\(e\left(\frac{9181}{34729}\right)\)	\(e\left(\frac{19765}{69458}\right)\)
\(\chi_{138917}(24,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{66049}{69458}\right)\)	\(e\left(\frac{53817}{69458}\right)\)	\(e\left(\frac{31320}{34729}\right)\)	\(e\left(\frac{17935}{69458}\right)\)	\(e\left(\frac{25204}{34729}\right)\)	\(e\left(\frac{6870}{34729}\right)\)	\(e\left(\frac{59231}{69458}\right)\)	\(e\left(\frac{19088}{34729}\right)\)	\(e\left(\frac{7263}{34729}\right)\)	\(e\left(\frac{24581}{34729}\right)\)
\(\chi_{138917}(25,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{44249}{69458}\right)\)	\(e\left(\frac{42039}{69458}\right)\)	\(e\left(\frac{9520}{34729}\right)\)	\(e\left(\frac{22439}{69458}\right)\)	\(e\left(\frac{8415}{34729}\right)\)	\(e\left(\frac{10338}{34729}\right)\)	\(e\left(\frac{63289}{69458}\right)\)	\(e\left(\frac{7310}{34729}\right)\)	\(e\left(\frac{33344}{34729}\right)\)	\(e\left(\frac{18427}{34729}\right)\)
\(\chi_{138917}(26,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{101965}{138916}\right)\)	\(e\left(\frac{49147}{138916}\right)\)	\(e\left(\frac{32507}{69458}\right)\)	\(e\left(\frac{65979}{138916}\right)\)	\(e\left(\frac{3049}{34729}\right)\)	\(e\left(\frac{3981}{34729}\right)\)	\(e\left(\frac{28063}{138916}\right)\)	\(e\left(\frac{49147}{69458}\right)\)	\(e\left(\frac{7257}{34729}\right)\)	\(e\left(\frac{26729}{69458}\right)\)
\(\chi_{138917}(27,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{118453}{138916}\right)\)	\(e\left(\frac{106459}{138916}\right)\)	\(e\left(\frac{48995}{69458}\right)\)	\(e\left(\frac{56659}{138916}\right)\)	\(e\left(\frac{21499}{34729}\right)\)	\(e\left(\frac{33333}{34729}\right)\)	\(e\left(\frac{77527}{138916}\right)\)	\(e\left(\frac{37001}{69458}\right)\)	\(e\left(\frac{9049}{34729}\right)\)	\(e\left(\frac{12445}{69458}\right)\)
\(\chi_{138917}(28,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{43479}{69458}\right)\)	\(e\left(\frac{15401}{69458}\right)\)	\(e\left(\frac{8750}{34729}\right)\)	\(e\left(\frac{54587}{69458}\right)\)	\(e\left(\frac{29440}{34729}\right)\)	\(e\left(\frac{11034}{34729}\right)\)	\(e\left(\frac{60979}{69458}\right)\)	\(e\left(\frac{15401}{34729}\right)\)	\(e\left(\frac{14304}{34729}\right)\)	\(e\left(\frac{33535}{34729}\right)\)
\(\chi_{138917}(29,\cdot)\)	138917.e	69458	yes	\(1\)	\(1\)	\(e\left(\frac{3483}{69458}\right)\)	\(e\left(\frac{66551}{69458}\right)\)	\(e\left(\frac{3483}{34729}\right)\)	\(e\left(\frac{61423}{69458}\right)\)	\(e\left(\frac{288}{34729}\right)\)	\(e\left(\frac{15434}{34729}\right)\)	\(e\left(\frac{10449}{69458}\right)\)	\(e\left(\frac{31822}{34729}\right)\)	\(e\left(\frac{32453}{34729}\right)\)	\(e\left(\frac{28451}{34729}\right)\)
\(\chi_{138917}(30,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{106887}{138916}\right)\)	\(e\left(\frac{93857}{138916}\right)\)	\(e\left(\frac{37429}{69458}\right)\)	\(e\left(\frac{39269}{138916}\right)\)	\(e\left(\frac{15457}{34729}\right)\)	\(e\left(\frac{3290}{34729}\right)\)	\(e\left(\frac{42829}{138916}\right)\)	\(e\left(\frac{24399}{69458}\right)\)	\(e\left(\frac{1810}{34729}\right)\)	\(e\left(\frac{53015}{69458}\right)\)
\(\chi_{138917}(31,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{62385}{138916}\right)\)	\(e\left(\frac{110539}{138916}\right)\)	\(e\left(\frac{62385}{69458}\right)\)	\(e\left(\frac{4571}{138916}\right)\)	\(e\left(\frac{8502}{34729}\right)\)	\(e\left(\frac{20065}{34729}\right)\)	\(e\left(\frac{48239}{138916}\right)\)	\(e\left(\frac{41081}{69458}\right)\)	\(e\left(\frac{16739}{34729}\right)\)	\(e\left(\frac{66343}{69458}\right)\)
\(\chi_{138917}(32,\cdot)\)	138917.f	138916	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{138916}\right)\)	\(e\left(\frac{104811}{138916}\right)\)	\(e\left(\frac{5}{69458}\right)\)	\(e\left(\frac{12871}{138916}\right)\)	\(e\left(\frac{26204}{34729}\right)\)	\(e\left(\frac{4508}{34729}\right)\)	\(e\left(\frac{15}{138916}\right)\)	\(e\left(\frac{35353}{69458}\right)\)	\(e\left(\frac{3219}{34729}\right)\)	\(e\left(\frac{36435}{69458}\right)\)

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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.