LMFDB - Group of Dirichlet characters of modulus 140659

Show commands: PariGP / SageMath

sage: H = DirichletGroup(140659)

pari: g = idealstar(,140659,2)

Character group

sage: G.order() pari: g.no
Order	=	140658
sage: H.invariants() pari: g.cyc
Structure	=	$C_{140658}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{140659}(3,\cdot)$

First 32 of 140658 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{140659}(1,\cdot)$	140659.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{140659}(2,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{11591}{46886}\right)$	$e\left(\frac{28717}{46886}\right)$	$e\left(\frac{11591}{23443}\right)$	$e\left(\frac{787}{3349}\right)$	$e\left(\frac{20154}{23443}\right)$	$e\left(\frac{32259}{46886}\right)$	$e\left(\frac{34773}{46886}\right)$	$e\left(\frac{5274}{23443}\right)$	$e\left(\frac{22609}{46886}\right)$	$e\left(\frac{17160}{23443}\right)$
$\chi_{140659}(3,\cdot)$	140659.bf	140658	yes	$-1$	$1$	$e\left(\frac{28717}{46886}\right)$	$e\left(\frac{1}{140658}\right)$	$e\left(\frac{5274}{23443}\right)$	$e\left(\frac{645}{3349}\right)$	$e\left(\frac{43076}{70329}\right)$	$e\left(\frac{42243}{46886}\right)$	$e\left(\frac{39265}{46886}\right)$	$e\left(\frac{1}{70329}\right)$	$e\left(\frac{37747}{46886}\right)$	$e\left(\frac{42302}{70329}\right)$
$\chi_{140659}(4,\cdot)$	140659.bc	23443	yes	$1$	$1$	$e\left(\frac{11591}{23443}\right)$	$e\left(\frac{5274}{23443}\right)$	$e\left(\frac{23182}{23443}\right)$	$e\left(\frac{1574}{3349}\right)$	$e\left(\frac{16865}{23443}\right)$	$e\left(\frac{8816}{23443}\right)$	$e\left(\frac{11330}{23443}\right)$	$e\left(\frac{10548}{23443}\right)$	$e\left(\frac{22609}{23443}\right)$	$e\left(\frac{10877}{23443}\right)$
$\chi_{140659}(5,\cdot)$	140659.w	3349	yes	$1$	$1$	$e\left(\frac{787}{3349}\right)$	$e\left(\frac{645}{3349}\right)$	$e\left(\frac{1574}{3349}\right)$	$e\left(\frac{1317}{3349}\right)$	$e\left(\frac{1432}{3349}\right)$	$e\left(\frac{1162}{3349}\right)$	$e\left(\frac{2361}{3349}\right)$	$e\left(\frac{1290}{3349}\right)$	$e\left(\frac{2104}{3349}\right)$	$e\left(\frac{974}{3349}\right)$
$\chi_{140659}(6,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{20154}{23443}\right)$	$e\left(\frac{43076}{70329}\right)$	$e\left(\frac{16865}{23443}\right)$	$e\left(\frac{1432}{3349}\right)$	$e\left(\frac{33209}{70329}\right)$	$e\left(\frac{13808}{23443}\right)$	$e\left(\frac{13576}{23443}\right)$	$e\left(\frac{15823}{70329}\right)$	$e\left(\frac{6735}{23443}\right)$	$e\left(\frac{23453}{70329}\right)$
$\chi_{140659}(7,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{32259}{46886}\right)$	$e\left(\frac{42243}{46886}\right)$	$e\left(\frac{8816}{23443}\right)$	$e\left(\frac{1162}{3349}\right)$	$e\left(\frac{13808}{23443}\right)$	$e\left(\frac{16553}{46886}\right)$	$e\left(\frac{3005}{46886}\right)$	$e\left(\frac{18800}{23443}\right)$	$e\left(\frac{1641}{46886}\right)$	$e\left(\frac{20711}{23443}\right)$
$\chi_{140659}(8,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{34773}{46886}\right)$	$e\left(\frac{39265}{46886}\right)$	$e\left(\frac{11330}{23443}\right)$	$e\left(\frac{2361}{3349}\right)$	$e\left(\frac{13576}{23443}\right)$	$e\left(\frac{3005}{46886}\right)$	$e\left(\frac{10547}{46886}\right)$	$e\left(\frac{15822}{23443}\right)$	$e\left(\frac{20941}{46886}\right)$	$e\left(\frac{4594}{23443}\right)$
$\chi_{140659}(9,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{5274}{23443}\right)$	$e\left(\frac{1}{70329}\right)$	$e\left(\frac{10548}{23443}\right)$	$e\left(\frac{1290}{3349}\right)$	$e\left(\frac{15823}{70329}\right)$	$e\left(\frac{18800}{23443}\right)$	$e\left(\frac{15822}{23443}\right)$	$e\left(\frac{2}{70329}\right)$	$e\left(\frac{14304}{23443}\right)$	$e\left(\frac{14275}{70329}\right)$
$\chi_{140659}(10,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{22609}{46886}\right)$	$e\left(\frac{37747}{46886}\right)$	$e\left(\frac{22609}{23443}\right)$	$e\left(\frac{2104}{3349}\right)$	$e\left(\frac{6735}{23443}\right)$	$e\left(\frac{1641}{46886}\right)$	$e\left(\frac{20941}{46886}\right)$	$e\left(\frac{14304}{23443}\right)$	$e\left(\frac{5179}{46886}\right)$	$e\left(\frac{535}{23443}\right)$
$\chi_{140659}(11,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{17160}{23443}\right)$	$e\left(\frac{42302}{70329}\right)$	$e\left(\frac{10877}{23443}\right)$	$e\left(\frac{974}{3349}\right)$	$e\left(\frac{23453}{70329}\right)$	$e\left(\frac{20711}{23443}\right)$	$e\left(\frac{4594}{23443}\right)$	$e\left(\frac{14275}{70329}\right)$	$e\left(\frac{535}{23443}\right)$	$e\left(\frac{16256}{70329}\right)$
$\chi_{140659}(12,\cdot)$	140659.bf	140658	yes	$-1$	$1$	$e\left(\frac{5013}{46886}\right)$	$e\left(\frac{31645}{140658}\right)$	$e\left(\frac{5013}{23443}\right)$	$e\left(\frac{2219}{3349}\right)$	$e\left(\frac{23342}{70329}\right)$	$e\left(\frac{12989}{46886}\right)$	$e\left(\frac{15039}{46886}\right)$	$e\left(\frac{31645}{70329}\right)$	$e\left(\frac{36079}{46886}\right)$	$e\left(\frac{4604}{70329}\right)$
$\chi_{140659}(13,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{19668}{23443}\right)$	$e\left(\frac{20353}{70329}\right)$	$e\left(\frac{15893}{23443}\right)$	$e\left(\frac{2559}{3349}\right)$	$e\left(\frac{9028}{70329}\right)$	$e\left(\frac{23197}{23443}\right)$	$e\left(\frac{12118}{23443}\right)$	$e\left(\frac{40706}{70329}\right)$	$e\left(\frac{14138}{23443}\right)$	$e\left(\frac{9976}{70329}\right)$
$\chi_{140659}(14,\cdot)$	140659.bc	23443	yes	$1$	$1$	$e\left(\frac{21925}{23443}\right)$	$e\left(\frac{12037}{23443}\right)$	$e\left(\frac{20407}{23443}\right)$	$e\left(\frac{1949}{3349}\right)$	$e\left(\frac{10519}{23443}\right)$	$e\left(\frac{963}{23443}\right)$	$e\left(\frac{18889}{23443}\right)$	$e\left(\frac{631}{23443}\right)$	$e\left(\frac{12125}{23443}\right)$	$e\left(\frac{14428}{23443}\right)$
$\chi_{140659}(15,\cdot)$	140659.bf	140658	yes	$-1$	$1$	$e\left(\frac{39735}{46886}\right)$	$e\left(\frac{27091}{140658}\right)$	$e\left(\frac{16292}{23443}\right)$	$e\left(\frac{1962}{3349}\right)$	$e\left(\frac{2819}{70329}\right)$	$e\left(\frac{11625}{46886}\right)$	$e\left(\frac{25433}{46886}\right)$	$e\left(\frac{27091}{70329}\right)$	$e\left(\frac{20317}{46886}\right)$	$e\left(\frac{62756}{70329}\right)$
$\chi_{140659}(16,\cdot)$	140659.bc	23443	yes	$1$	$1$	$e\left(\frac{23182}{23443}\right)$	$e\left(\frac{10548}{23443}\right)$	$e\left(\frac{22921}{23443}\right)$	$e\left(\frac{3148}{3349}\right)$	$e\left(\frac{10287}{23443}\right)$	$e\left(\frac{17632}{23443}\right)$	$e\left(\frac{22660}{23443}\right)$	$e\left(\frac{21096}{23443}\right)$	$e\left(\frac{21775}{23443}\right)$	$e\left(\frac{21754}{23443}\right)$
$\chi_{140659}(17,\cdot)$	140659.ba	10047	yes	$1$	$1$	$e\left(\frac{2973}{3349}\right)$	$e\left(\frac{433}{10047}\right)$	$e\left(\frac{2597}{3349}\right)$	$e\left(\frac{1707}{3349}\right)$	$e\left(\frac{9352}{10047}\right)$	$e\left(\frac{2330}{3349}\right)$	$e\left(\frac{2221}{3349}\right)$	$e\left(\frac{866}{10047}\right)$	$e\left(\frac{1331}{3349}\right)$	$e\left(\frac{2170}{10047}\right)$
$\chi_{140659}(18,\cdot)$	140659.bf	140658	yes	$-1$	$1$	$e\left(\frac{22139}{46886}\right)$	$e\left(\frac{86153}{140658}\right)$	$e\left(\frac{22139}{23443}\right)$	$e\left(\frac{2077}{3349}\right)$	$e\left(\frac{5956}{70329}\right)$	$e\left(\frac{22973}{46886}\right)$	$e\left(\frac{19531}{46886}\right)$	$e\left(\frac{15824}{70329}\right)$	$e\left(\frac{4331}{46886}\right)$	$e\left(\frac{65755}{70329}\right)$
$\chi_{140659}(19,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{835}{23443}\right)$	$e\left(\frac{25679}{70329}\right)$	$e\left(\frac{1670}{23443}\right)$	$e\left(\frac{951}{3349}\right)$	$e\left(\frac{28184}{70329}\right)$	$e\left(\frac{3501}{23443}\right)$	$e\left(\frac{2505}{23443}\right)$	$e\left(\frac{51358}{70329}\right)$	$e\left(\frac{7492}{23443}\right)$	$e\left(\frac{12977}{70329}\right)$
$\chi_{140659}(20,\cdot)$	140659.bc	23443	yes	$1$	$1$	$e\left(\frac{17100}{23443}\right)$	$e\left(\frac{9789}{23443}\right)$	$e\left(\frac{10757}{23443}\right)$	$e\left(\frac{2891}{3349}\right)$	$e\left(\frac{3446}{23443}\right)$	$e\left(\frac{16950}{23443}\right)$	$e\left(\frac{4414}{23443}\right)$	$e\left(\frac{19578}{23443}\right)$	$e\left(\frac{13894}{23443}\right)$	$e\left(\frac{17695}{23443}\right)$
$\chi_{140659}(21,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{7045}{23443}\right)$	$e\left(\frac{63365}{70329}\right)$	$e\left(\frac{14090}{23443}\right)$	$e\left(\frac{1807}{3349}\right)$	$e\left(\frac{14171}{70329}\right)$	$e\left(\frac{5955}{23443}\right)$	$e\left(\frac{21135}{23443}\right)$	$e\left(\frac{56401}{70329}\right)$	$e\left(\frac{19694}{23443}\right)$	$e\left(\frac{34106}{70329}\right)$
$\chi_{140659}(22,\cdot)$	140659.bf	140658	yes	$-1$	$1$	$e\left(\frac{45911}{46886}\right)$	$e\left(\frac{30097}{140658}\right)$	$e\left(\frac{22468}{23443}\right)$	$e\left(\frac{1761}{3349}\right)$	$e\left(\frac{13586}{70329}\right)$	$e\left(\frac{26795}{46886}\right)$	$e\left(\frac{43961}{46886}\right)$	$e\left(\frac{30097}{70329}\right)$	$e\left(\frac{23679}{46886}\right)$	$e\left(\frac{67736}{70329}\right)$
$\chi_{140659}(23,\cdot)$	140659.w	3349	yes	$1$	$1$	$e\left(\frac{1668}{3349}\right)$	$e\left(\frac{1533}{3349}\right)$	$e\left(\frac{3336}{3349}\right)$	$e\left(\frac{1370}{3349}\right)$	$e\left(\frac{3201}{3349}\right)$	$e\left(\frac{67}{3349}\right)$	$e\left(\frac{1655}{3349}\right)$	$e\left(\frac{3066}{3349}\right)$	$e\left(\frac{3038}{3349}\right)$	$e\left(\frac{1209}{3349}\right)$
$\chi_{140659}(24,\cdot)$	140659.ba	10047	yes	$1$	$1$	$e\left(\frac{1186}{3349}\right)$	$e\left(\frac{8414}{10047}\right)$	$e\left(\frac{2372}{3349}\right)$	$e\left(\frac{3006}{3349}\right)$	$e\left(\frac{1925}{10047}\right)$	$e\left(\frac{3232}{3349}\right)$	$e\left(\frac{209}{3349}\right)$	$e\left(\frac{6781}{10047}\right)$	$e\left(\frac{843}{3349}\right)$	$e\left(\frac{8012}{10047}\right)$
$\chi_{140659}(25,\cdot)$	140659.w	3349	yes	$1$	$1$	$e\left(\frac{1574}{3349}\right)$	$e\left(\frac{1290}{3349}\right)$	$e\left(\frac{3148}{3349}\right)$	$e\left(\frac{2634}{3349}\right)$	$e\left(\frac{2864}{3349}\right)$	$e\left(\frac{2324}{3349}\right)$	$e\left(\frac{1373}{3349}\right)$	$e\left(\frac{2580}{3349}\right)$	$e\left(\frac{859}{3349}\right)$	$e\left(\frac{1948}{3349}\right)$
$\chi_{140659}(26,\cdot)$	140659.bf	140658	yes	$-1$	$1$	$e\left(\frac{4041}{46886}\right)$	$e\left(\frac{126857}{140658}\right)$	$e\left(\frac{4041}{23443}\right)$	$e\left(\frac{3346}{3349}\right)$	$e\left(\frac{69490}{70329}\right)$	$e\left(\frac{31767}{46886}\right)$	$e\left(\frac{12123}{46886}\right)$	$e\left(\frac{56528}{70329}\right)$	$e\left(\frac{3999}{46886}\right)$	$e\left(\frac{61456}{70329}\right)$
$\chi_{140659}(27,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{39265}{46886}\right)$	$e\left(\frac{1}{46886}\right)$	$e\left(\frac{15822}{23443}\right)$	$e\left(\frac{1935}{3349}\right)$	$e\left(\frac{19633}{23443}\right)$	$e\left(\frac{32957}{46886}\right)$	$e\left(\frac{24023}{46886}\right)$	$e\left(\frac{1}{23443}\right)$	$e\left(\frac{19469}{46886}\right)$	$e\left(\frac{18859}{23443}\right)$
$\chi_{140659}(28,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{8555}{46886}\right)$	$e\left(\frac{5905}{46886}\right)$	$e\left(\frac{8555}{23443}\right)$	$e\left(\frac{2736}{3349}\right)$	$e\left(\frac{7230}{23443}\right)$	$e\left(\frac{34185}{46886}\right)$	$e\left(\frac{25665}{46886}\right)$	$e\left(\frac{5905}{23443}\right)$	$e\left(\frac{46859}{46886}\right)$	$e\left(\frac{8145}{23443}\right)$
$\chi_{140659}(29,\cdot)$	140659.bc	23443	yes	$1$	$1$	$e\left(\frac{9293}{23443}\right)$	$e\left(\frac{331}{23443}\right)$	$e\left(\frac{18586}{23443}\right)$	$e\left(\frac{1652}{3349}\right)$	$e\left(\frac{9624}{23443}\right)$	$e\left(\frac{7772}{23443}\right)$	$e\left(\frac{4436}{23443}\right)$	$e\left(\frac{662}{23443}\right)$	$e\left(\frac{20857}{23443}\right)$	$e\left(\frac{12982}{23443}\right)$
$\chi_{140659}(30,\cdot)$	140659.be	70329	yes	$1$	$1$	$e\left(\frac{2220}{23443}\right)$	$e\left(\frac{56621}{70329}\right)$	$e\left(\frac{4440}{23443}\right)$	$e\left(\frac{2749}{3349}\right)$	$e\left(\frac{63281}{70329}\right)$	$e\left(\frac{21942}{23443}\right)$	$e\left(\frac{6660}{23443}\right)$	$e\left(\frac{42913}{70329}\right)$	$e\left(\frac{21463}{23443}\right)$	$e\left(\frac{43907}{70329}\right)$
$\chi_{140659}(31,\cdot)$	140659.bc	23443	yes	$1$	$1$	$e\left(\frac{3319}{23443}\right)$	$e\left(\frac{7333}{23443}\right)$	$e\left(\frac{6638}{23443}\right)$	$e\left(\frac{2633}{3349}\right)$	$e\left(\frac{10652}{23443}\right)$	$e\left(\frac{23237}{23443}\right)$	$e\left(\frac{9957}{23443}\right)$	$e\left(\frac{14666}{23443}\right)$	$e\left(\frac{21750}{23443}\right)$	$e\left(\frac{5580}{23443}\right)$
$\chi_{140659}(32,\cdot)$	140659.bd	46886	yes	$-1$	$1$	$e\left(\frac{11069}{46886}\right)$	$e\left(\frac{2927}{46886}\right)$	$e\left(\frac{11069}{23443}\right)$	$e\left(\frac{586}{3349}\right)$	$e\left(\frac{6998}{23443}\right)$	$e\left(\frac{20637}{46886}\right)$	$e\left(\frac{33207}{46886}\right)$	$e\left(\frac{2927}{23443}\right)$	$e\left(\frac{19273}{46886}\right)$	$e\left(\frac{15471}{23443}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Modulus	$140659$
Structure	\(C_{140658}\)
Order	$140658$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{140659}(1,\cdot)\)	140659.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{140659}(2,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{11591}{46886}\right)\)	\(e\left(\frac{28717}{46886}\right)\)	\(e\left(\frac{11591}{23443}\right)\)	\(e\left(\frac{787}{3349}\right)\)	\(e\left(\frac{20154}{23443}\right)\)	\(e\left(\frac{32259}{46886}\right)\)	\(e\left(\frac{34773}{46886}\right)\)	\(e\left(\frac{5274}{23443}\right)\)	\(e\left(\frac{22609}{46886}\right)\)	\(e\left(\frac{17160}{23443}\right)\)
\(\chi_{140659}(3,\cdot)\)	140659.bf	140658	yes	\(-1\)	\(1\)	\(e\left(\frac{28717}{46886}\right)\)	\(e\left(\frac{1}{140658}\right)\)	\(e\left(\frac{5274}{23443}\right)\)	\(e\left(\frac{645}{3349}\right)\)	\(e\left(\frac{43076}{70329}\right)\)	\(e\left(\frac{42243}{46886}\right)\)	\(e\left(\frac{39265}{46886}\right)\)	\(e\left(\frac{1}{70329}\right)\)	\(e\left(\frac{37747}{46886}\right)\)	\(e\left(\frac{42302}{70329}\right)\)
\(\chi_{140659}(4,\cdot)\)	140659.bc	23443	yes	\(1\)	\(1\)	\(e\left(\frac{11591}{23443}\right)\)	\(e\left(\frac{5274}{23443}\right)\)	\(e\left(\frac{23182}{23443}\right)\)	\(e\left(\frac{1574}{3349}\right)\)	\(e\left(\frac{16865}{23443}\right)\)	\(e\left(\frac{8816}{23443}\right)\)	\(e\left(\frac{11330}{23443}\right)\)	\(e\left(\frac{10548}{23443}\right)\)	\(e\left(\frac{22609}{23443}\right)\)	\(e\left(\frac{10877}{23443}\right)\)
\(\chi_{140659}(5,\cdot)\)	140659.w	3349	yes	\(1\)	\(1\)	\(e\left(\frac{787}{3349}\right)\)	\(e\left(\frac{645}{3349}\right)\)	\(e\left(\frac{1574}{3349}\right)\)	\(e\left(\frac{1317}{3349}\right)\)	\(e\left(\frac{1432}{3349}\right)\)	\(e\left(\frac{1162}{3349}\right)\)	\(e\left(\frac{2361}{3349}\right)\)	\(e\left(\frac{1290}{3349}\right)\)	\(e\left(\frac{2104}{3349}\right)\)	\(e\left(\frac{974}{3349}\right)\)
\(\chi_{140659}(6,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{20154}{23443}\right)\)	\(e\left(\frac{43076}{70329}\right)\)	\(e\left(\frac{16865}{23443}\right)\)	\(e\left(\frac{1432}{3349}\right)\)	\(e\left(\frac{33209}{70329}\right)\)	\(e\left(\frac{13808}{23443}\right)\)	\(e\left(\frac{13576}{23443}\right)\)	\(e\left(\frac{15823}{70329}\right)\)	\(e\left(\frac{6735}{23443}\right)\)	\(e\left(\frac{23453}{70329}\right)\)
\(\chi_{140659}(7,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{32259}{46886}\right)\)	\(e\left(\frac{42243}{46886}\right)\)	\(e\left(\frac{8816}{23443}\right)\)	\(e\left(\frac{1162}{3349}\right)\)	\(e\left(\frac{13808}{23443}\right)\)	\(e\left(\frac{16553}{46886}\right)\)	\(e\left(\frac{3005}{46886}\right)\)	\(e\left(\frac{18800}{23443}\right)\)	\(e\left(\frac{1641}{46886}\right)\)	\(e\left(\frac{20711}{23443}\right)\)
\(\chi_{140659}(8,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{34773}{46886}\right)\)	\(e\left(\frac{39265}{46886}\right)\)	\(e\left(\frac{11330}{23443}\right)\)	\(e\left(\frac{2361}{3349}\right)\)	\(e\left(\frac{13576}{23443}\right)\)	\(e\left(\frac{3005}{46886}\right)\)	\(e\left(\frac{10547}{46886}\right)\)	\(e\left(\frac{15822}{23443}\right)\)	\(e\left(\frac{20941}{46886}\right)\)	\(e\left(\frac{4594}{23443}\right)\)
\(\chi_{140659}(9,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{5274}{23443}\right)\)	\(e\left(\frac{1}{70329}\right)\)	\(e\left(\frac{10548}{23443}\right)\)	\(e\left(\frac{1290}{3349}\right)\)	\(e\left(\frac{15823}{70329}\right)\)	\(e\left(\frac{18800}{23443}\right)\)	\(e\left(\frac{15822}{23443}\right)\)	\(e\left(\frac{2}{70329}\right)\)	\(e\left(\frac{14304}{23443}\right)\)	\(e\left(\frac{14275}{70329}\right)\)
\(\chi_{140659}(10,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{22609}{46886}\right)\)	\(e\left(\frac{37747}{46886}\right)\)	\(e\left(\frac{22609}{23443}\right)\)	\(e\left(\frac{2104}{3349}\right)\)	\(e\left(\frac{6735}{23443}\right)\)	\(e\left(\frac{1641}{46886}\right)\)	\(e\left(\frac{20941}{46886}\right)\)	\(e\left(\frac{14304}{23443}\right)\)	\(e\left(\frac{5179}{46886}\right)\)	\(e\left(\frac{535}{23443}\right)\)
\(\chi_{140659}(11,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{17160}{23443}\right)\)	\(e\left(\frac{42302}{70329}\right)\)	\(e\left(\frac{10877}{23443}\right)\)	\(e\left(\frac{974}{3349}\right)\)	\(e\left(\frac{23453}{70329}\right)\)	\(e\left(\frac{20711}{23443}\right)\)	\(e\left(\frac{4594}{23443}\right)\)	\(e\left(\frac{14275}{70329}\right)\)	\(e\left(\frac{535}{23443}\right)\)	\(e\left(\frac{16256}{70329}\right)\)
\(\chi_{140659}(12,\cdot)\)	140659.bf	140658	yes	\(-1\)	\(1\)	\(e\left(\frac{5013}{46886}\right)\)	\(e\left(\frac{31645}{140658}\right)\)	\(e\left(\frac{5013}{23443}\right)\)	\(e\left(\frac{2219}{3349}\right)\)	\(e\left(\frac{23342}{70329}\right)\)	\(e\left(\frac{12989}{46886}\right)\)	\(e\left(\frac{15039}{46886}\right)\)	\(e\left(\frac{31645}{70329}\right)\)	\(e\left(\frac{36079}{46886}\right)\)	\(e\left(\frac{4604}{70329}\right)\)
\(\chi_{140659}(13,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{19668}{23443}\right)\)	\(e\left(\frac{20353}{70329}\right)\)	\(e\left(\frac{15893}{23443}\right)\)	\(e\left(\frac{2559}{3349}\right)\)	\(e\left(\frac{9028}{70329}\right)\)	\(e\left(\frac{23197}{23443}\right)\)	\(e\left(\frac{12118}{23443}\right)\)	\(e\left(\frac{40706}{70329}\right)\)	\(e\left(\frac{14138}{23443}\right)\)	\(e\left(\frac{9976}{70329}\right)\)
\(\chi_{140659}(14,\cdot)\)	140659.bc	23443	yes	\(1\)	\(1\)	\(e\left(\frac{21925}{23443}\right)\)	\(e\left(\frac{12037}{23443}\right)\)	\(e\left(\frac{20407}{23443}\right)\)	\(e\left(\frac{1949}{3349}\right)\)	\(e\left(\frac{10519}{23443}\right)\)	\(e\left(\frac{963}{23443}\right)\)	\(e\left(\frac{18889}{23443}\right)\)	\(e\left(\frac{631}{23443}\right)\)	\(e\left(\frac{12125}{23443}\right)\)	\(e\left(\frac{14428}{23443}\right)\)
\(\chi_{140659}(15,\cdot)\)	140659.bf	140658	yes	\(-1\)	\(1\)	\(e\left(\frac{39735}{46886}\right)\)	\(e\left(\frac{27091}{140658}\right)\)	\(e\left(\frac{16292}{23443}\right)\)	\(e\left(\frac{1962}{3349}\right)\)	\(e\left(\frac{2819}{70329}\right)\)	\(e\left(\frac{11625}{46886}\right)\)	\(e\left(\frac{25433}{46886}\right)\)	\(e\left(\frac{27091}{70329}\right)\)	\(e\left(\frac{20317}{46886}\right)\)	\(e\left(\frac{62756}{70329}\right)\)
\(\chi_{140659}(16,\cdot)\)	140659.bc	23443	yes	\(1\)	\(1\)	\(e\left(\frac{23182}{23443}\right)\)	\(e\left(\frac{10548}{23443}\right)\)	\(e\left(\frac{22921}{23443}\right)\)	\(e\left(\frac{3148}{3349}\right)\)	\(e\left(\frac{10287}{23443}\right)\)	\(e\left(\frac{17632}{23443}\right)\)	\(e\left(\frac{22660}{23443}\right)\)	\(e\left(\frac{21096}{23443}\right)\)	\(e\left(\frac{21775}{23443}\right)\)	\(e\left(\frac{21754}{23443}\right)\)
\(\chi_{140659}(17,\cdot)\)	140659.ba	10047	yes	\(1\)	\(1\)	\(e\left(\frac{2973}{3349}\right)\)	\(e\left(\frac{433}{10047}\right)\)	\(e\left(\frac{2597}{3349}\right)\)	\(e\left(\frac{1707}{3349}\right)\)	\(e\left(\frac{9352}{10047}\right)\)	\(e\left(\frac{2330}{3349}\right)\)	\(e\left(\frac{2221}{3349}\right)\)	\(e\left(\frac{866}{10047}\right)\)	\(e\left(\frac{1331}{3349}\right)\)	\(e\left(\frac{2170}{10047}\right)\)
\(\chi_{140659}(18,\cdot)\)	140659.bf	140658	yes	\(-1\)	\(1\)	\(e\left(\frac{22139}{46886}\right)\)	\(e\left(\frac{86153}{140658}\right)\)	\(e\left(\frac{22139}{23443}\right)\)	\(e\left(\frac{2077}{3349}\right)\)	\(e\left(\frac{5956}{70329}\right)\)	\(e\left(\frac{22973}{46886}\right)\)	\(e\left(\frac{19531}{46886}\right)\)	\(e\left(\frac{15824}{70329}\right)\)	\(e\left(\frac{4331}{46886}\right)\)	\(e\left(\frac{65755}{70329}\right)\)
\(\chi_{140659}(19,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{835}{23443}\right)\)	\(e\left(\frac{25679}{70329}\right)\)	\(e\left(\frac{1670}{23443}\right)\)	\(e\left(\frac{951}{3349}\right)\)	\(e\left(\frac{28184}{70329}\right)\)	\(e\left(\frac{3501}{23443}\right)\)	\(e\left(\frac{2505}{23443}\right)\)	\(e\left(\frac{51358}{70329}\right)\)	\(e\left(\frac{7492}{23443}\right)\)	\(e\left(\frac{12977}{70329}\right)\)
\(\chi_{140659}(20,\cdot)\)	140659.bc	23443	yes	\(1\)	\(1\)	\(e\left(\frac{17100}{23443}\right)\)	\(e\left(\frac{9789}{23443}\right)\)	\(e\left(\frac{10757}{23443}\right)\)	\(e\left(\frac{2891}{3349}\right)\)	\(e\left(\frac{3446}{23443}\right)\)	\(e\left(\frac{16950}{23443}\right)\)	\(e\left(\frac{4414}{23443}\right)\)	\(e\left(\frac{19578}{23443}\right)\)	\(e\left(\frac{13894}{23443}\right)\)	\(e\left(\frac{17695}{23443}\right)\)
\(\chi_{140659}(21,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{7045}{23443}\right)\)	\(e\left(\frac{63365}{70329}\right)\)	\(e\left(\frac{14090}{23443}\right)\)	\(e\left(\frac{1807}{3349}\right)\)	\(e\left(\frac{14171}{70329}\right)\)	\(e\left(\frac{5955}{23443}\right)\)	\(e\left(\frac{21135}{23443}\right)\)	\(e\left(\frac{56401}{70329}\right)\)	\(e\left(\frac{19694}{23443}\right)\)	\(e\left(\frac{34106}{70329}\right)\)
\(\chi_{140659}(22,\cdot)\)	140659.bf	140658	yes	\(-1\)	\(1\)	\(e\left(\frac{45911}{46886}\right)\)	\(e\left(\frac{30097}{140658}\right)\)	\(e\left(\frac{22468}{23443}\right)\)	\(e\left(\frac{1761}{3349}\right)\)	\(e\left(\frac{13586}{70329}\right)\)	\(e\left(\frac{26795}{46886}\right)\)	\(e\left(\frac{43961}{46886}\right)\)	\(e\left(\frac{30097}{70329}\right)\)	\(e\left(\frac{23679}{46886}\right)\)	\(e\left(\frac{67736}{70329}\right)\)
\(\chi_{140659}(23,\cdot)\)	140659.w	3349	yes	\(1\)	\(1\)	\(e\left(\frac{1668}{3349}\right)\)	\(e\left(\frac{1533}{3349}\right)\)	\(e\left(\frac{3336}{3349}\right)\)	\(e\left(\frac{1370}{3349}\right)\)	\(e\left(\frac{3201}{3349}\right)\)	\(e\left(\frac{67}{3349}\right)\)	\(e\left(\frac{1655}{3349}\right)\)	\(e\left(\frac{3066}{3349}\right)\)	\(e\left(\frac{3038}{3349}\right)\)	\(e\left(\frac{1209}{3349}\right)\)
\(\chi_{140659}(24,\cdot)\)	140659.ba	10047	yes	\(1\)	\(1\)	\(e\left(\frac{1186}{3349}\right)\)	\(e\left(\frac{8414}{10047}\right)\)	\(e\left(\frac{2372}{3349}\right)\)	\(e\left(\frac{3006}{3349}\right)\)	\(e\left(\frac{1925}{10047}\right)\)	\(e\left(\frac{3232}{3349}\right)\)	\(e\left(\frac{209}{3349}\right)\)	\(e\left(\frac{6781}{10047}\right)\)	\(e\left(\frac{843}{3349}\right)\)	\(e\left(\frac{8012}{10047}\right)\)
\(\chi_{140659}(25,\cdot)\)	140659.w	3349	yes	\(1\)	\(1\)	\(e\left(\frac{1574}{3349}\right)\)	\(e\left(\frac{1290}{3349}\right)\)	\(e\left(\frac{3148}{3349}\right)\)	\(e\left(\frac{2634}{3349}\right)\)	\(e\left(\frac{2864}{3349}\right)\)	\(e\left(\frac{2324}{3349}\right)\)	\(e\left(\frac{1373}{3349}\right)\)	\(e\left(\frac{2580}{3349}\right)\)	\(e\left(\frac{859}{3349}\right)\)	\(e\left(\frac{1948}{3349}\right)\)
\(\chi_{140659}(26,\cdot)\)	140659.bf	140658	yes	\(-1\)	\(1\)	\(e\left(\frac{4041}{46886}\right)\)	\(e\left(\frac{126857}{140658}\right)\)	\(e\left(\frac{4041}{23443}\right)\)	\(e\left(\frac{3346}{3349}\right)\)	\(e\left(\frac{69490}{70329}\right)\)	\(e\left(\frac{31767}{46886}\right)\)	\(e\left(\frac{12123}{46886}\right)\)	\(e\left(\frac{56528}{70329}\right)\)	\(e\left(\frac{3999}{46886}\right)\)	\(e\left(\frac{61456}{70329}\right)\)
\(\chi_{140659}(27,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{39265}{46886}\right)\)	\(e\left(\frac{1}{46886}\right)\)	\(e\left(\frac{15822}{23443}\right)\)	\(e\left(\frac{1935}{3349}\right)\)	\(e\left(\frac{19633}{23443}\right)\)	\(e\left(\frac{32957}{46886}\right)\)	\(e\left(\frac{24023}{46886}\right)\)	\(e\left(\frac{1}{23443}\right)\)	\(e\left(\frac{19469}{46886}\right)\)	\(e\left(\frac{18859}{23443}\right)\)
\(\chi_{140659}(28,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{8555}{46886}\right)\)	\(e\left(\frac{5905}{46886}\right)\)	\(e\left(\frac{8555}{23443}\right)\)	\(e\left(\frac{2736}{3349}\right)\)	\(e\left(\frac{7230}{23443}\right)\)	\(e\left(\frac{34185}{46886}\right)\)	\(e\left(\frac{25665}{46886}\right)\)	\(e\left(\frac{5905}{23443}\right)\)	\(e\left(\frac{46859}{46886}\right)\)	\(e\left(\frac{8145}{23443}\right)\)
\(\chi_{140659}(29,\cdot)\)	140659.bc	23443	yes	\(1\)	\(1\)	\(e\left(\frac{9293}{23443}\right)\)	\(e\left(\frac{331}{23443}\right)\)	\(e\left(\frac{18586}{23443}\right)\)	\(e\left(\frac{1652}{3349}\right)\)	\(e\left(\frac{9624}{23443}\right)\)	\(e\left(\frac{7772}{23443}\right)\)	\(e\left(\frac{4436}{23443}\right)\)	\(e\left(\frac{662}{23443}\right)\)	\(e\left(\frac{20857}{23443}\right)\)	\(e\left(\frac{12982}{23443}\right)\)
\(\chi_{140659}(30,\cdot)\)	140659.be	70329	yes	\(1\)	\(1\)	\(e\left(\frac{2220}{23443}\right)\)	\(e\left(\frac{56621}{70329}\right)\)	\(e\left(\frac{4440}{23443}\right)\)	\(e\left(\frac{2749}{3349}\right)\)	\(e\left(\frac{63281}{70329}\right)\)	\(e\left(\frac{21942}{23443}\right)\)	\(e\left(\frac{6660}{23443}\right)\)	\(e\left(\frac{42913}{70329}\right)\)	\(e\left(\frac{21463}{23443}\right)\)	\(e\left(\frac{43907}{70329}\right)\)
\(\chi_{140659}(31,\cdot)\)	140659.bc	23443	yes	\(1\)	\(1\)	\(e\left(\frac{3319}{23443}\right)\)	\(e\left(\frac{7333}{23443}\right)\)	\(e\left(\frac{6638}{23443}\right)\)	\(e\left(\frac{2633}{3349}\right)\)	\(e\left(\frac{10652}{23443}\right)\)	\(e\left(\frac{23237}{23443}\right)\)	\(e\left(\frac{9957}{23443}\right)\)	\(e\left(\frac{14666}{23443}\right)\)	\(e\left(\frac{21750}{23443}\right)\)	\(e\left(\frac{5580}{23443}\right)\)
\(\chi_{140659}(32,\cdot)\)	140659.bd	46886	yes	\(-1\)	\(1\)	\(e\left(\frac{11069}{46886}\right)\)	\(e\left(\frac{2927}{46886}\right)\)	\(e\left(\frac{11069}{23443}\right)\)	\(e\left(\frac{586}{3349}\right)\)	\(e\left(\frac{6998}{23443}\right)\)	\(e\left(\frac{20637}{46886}\right)\)	\(e\left(\frac{33207}{46886}\right)\)	\(e\left(\frac{2927}{23443}\right)\)	\(e\left(\frac{19273}{46886}\right)\)	\(e\left(\frac{15471}{23443}\right)\)

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Character group

First 32 of 140658 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.