LMFDB - Group of Dirichlet characters of modulus 61969

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(61969)

gp:g = idealstar(,61969,2)

magma:G = FullDirichletGroup(61969);

Character group

Order	=	59940	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{6}\times C_{9990}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{61969}(53974,\cdot)$, $\chi_{61969}(7999,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 59940 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{61969}(1,\cdot)$	61969.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{61969}(2,\cdot)$	61969.fn	1665	yes	$1$	$1$	$e\left(\frac{211}{555}\right)$	$e\left(\frac{92}{1665}\right)$	$e\left(\frac{422}{555}\right)$	$e\left(\frac{142}{333}\right)$	$e\left(\frac{145}{333}\right)$	$e\left(\frac{217}{555}\right)$	$e\left(\frac{26}{185}\right)$	$e\left(\frac{184}{1665}\right)$	$e\left(\frac{1343}{1665}\right)$	$e\left(\frac{1316}{1665}\right)$
$\chi_{61969}(3,\cdot)$	61969.gq	9990	yes	$1$	$1$	$e\left(\frac{92}{1665}\right)$	$e\left(\frac{169}{4995}\right)$	$e\left(\frac{184}{1665}\right)$	$e\left(\frac{992}{999}\right)$	$e\left(\frac{89}{999}\right)$	$e\left(\frac{1123}{3330}\right)$	$e\left(\frac{92}{555}\right)$	$e\left(\frac{338}{4995}\right)$	$e\left(\frac{241}{4995}\right)$	$e\left(\frac{7079}{9990}\right)$
$\chi_{61969}(4,\cdot)$	61969.fn	1665	yes	$1$	$1$	$e\left(\frac{422}{555}\right)$	$e\left(\frac{184}{1665}\right)$	$e\left(\frac{289}{555}\right)$	$e\left(\frac{284}{333}\right)$	$e\left(\frac{290}{333}\right)$	$e\left(\frac{434}{555}\right)$	$e\left(\frac{52}{185}\right)$	$e\left(\frac{368}{1665}\right)$	$e\left(\frac{1021}{1665}\right)$	$e\left(\frac{967}{1665}\right)$
$\chi_{61969}(5,\cdot)$	61969.ey	999	yes	$1$	$1$	$e\left(\frac{142}{333}\right)$	$e\left(\frac{992}{999}\right)$	$e\left(\frac{284}{333}\right)$	$e\left(\frac{98}{999}\right)$	$e\left(\frac{419}{999}\right)$	$e\left(\frac{4}{333}\right)$	$e\left(\frac{31}{111}\right)$	$e\left(\frac{985}{999}\right)$	$e\left(\frac{524}{999}\right)$	$e\left(\frac{479}{999}\right)$
$\chi_{61969}(6,\cdot)$	61969.fs	1998	yes	$1$	$1$	$e\left(\frac{145}{333}\right)$	$e\left(\frac{89}{999}\right)$	$e\left(\frac{290}{333}\right)$	$e\left(\frac{419}{999}\right)$	$e\left(\frac{524}{999}\right)$	$e\left(\frac{485}{666}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{178}{999}\right)$	$e\left(\frac{854}{999}\right)$	$e\left(\frac{997}{1998}\right)$
$\chi_{61969}(7,\cdot)$	61969.fz	3330	yes	$-1$	$1$	$e\left(\frac{217}{555}\right)$	$e\left(\frac{1123}{3330}\right)$	$e\left(\frac{434}{555}\right)$	$e\left(\frac{4}{333}\right)$	$e\left(\frac{485}{666}\right)$	$e\left(\frac{31}{370}\right)$	$e\left(\frac{32}{185}\right)$	$e\left(\frac{1123}{1665}\right)$	$e\left(\frac{671}{1665}\right)$	$e\left(\frac{1022}{1665}\right)$
$\chi_{61969}(8,\cdot)$	61969.en	555	yes	$1$	$1$	$e\left(\frac{26}{185}\right)$	$e\left(\frac{92}{555}\right)$	$e\left(\frac{52}{185}\right)$	$e\left(\frac{31}{111}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{32}{185}\right)$	$e\left(\frac{78}{185}\right)$	$e\left(\frac{184}{555}\right)$	$e\left(\frac{233}{555}\right)$	$e\left(\frac{206}{555}\right)$
$\chi_{61969}(9,\cdot)$	61969.gj	4995	yes	$1$	$1$	$e\left(\frac{184}{1665}\right)$	$e\left(\frac{338}{4995}\right)$	$e\left(\frac{368}{1665}\right)$	$e\left(\frac{985}{999}\right)$	$e\left(\frac{178}{999}\right)$	$e\left(\frac{1123}{1665}\right)$	$e\left(\frac{184}{555}\right)$	$e\left(\frac{676}{4995}\right)$	$e\left(\frac{482}{4995}\right)$	$e\left(\frac{2084}{4995}\right)$
$\chi_{61969}(10,\cdot)$	61969.gk	4995	yes	$1$	$1$	$e\left(\frac{1343}{1665}\right)$	$e\left(\frac{241}{4995}\right)$	$e\left(\frac{1021}{1665}\right)$	$e\left(\frac{524}{999}\right)$	$e\left(\frac{854}{999}\right)$	$e\left(\frac{671}{1665}\right)$	$e\left(\frac{233}{555}\right)$	$e\left(\frac{482}{4995}\right)$	$e\left(\frac{1654}{4995}\right)$	$e\left(\frac{1348}{4995}\right)$
$\chi_{61969}(11,\cdot)$	61969.gt	9990	yes	$-1$	$1$	$e\left(\frac{1316}{1665}\right)$	$e\left(\frac{7079}{9990}\right)$	$e\left(\frac{967}{1665}\right)$	$e\left(\frac{479}{999}\right)$	$e\left(\frac{997}{1998}\right)$	$e\left(\frac{1022}{1665}\right)$	$e\left(\frac{206}{555}\right)$	$e\left(\frac{2084}{4995}\right)$	$e\left(\frac{1348}{4995}\right)$	$e\left(\frac{3677}{9990}\right)$
$\chi_{61969}(12,\cdot)$	61969.gq	9990	yes	$1$	$1$	$e\left(\frac{1358}{1665}\right)$	$e\left(\frac{721}{4995}\right)$	$e\left(\frac{1051}{1665}\right)$	$e\left(\frac{845}{999}\right)$	$e\left(\frac{959}{999}\right)$	$e\left(\frac{397}{3330}\right)$	$e\left(\frac{248}{555}\right)$	$e\left(\frac{1442}{4995}\right)$	$e\left(\frac{3304}{4995}\right)$	$e\left(\frac{2891}{9990}\right)$
$\chi_{61969}(13,\cdot)$	61969.gb	3330	yes	$-1$	$1$	$e\left(\frac{274}{555}\right)$	$e\left(\frac{2551}{3330}\right)$	$e\left(\frac{548}{555}\right)$	$e\left(\frac{247}{333}\right)$	$e\left(\frac{173}{666}\right)$	$e\left(\frac{323}{555}\right)$	$e\left(\frac{89}{185}\right)$	$e\left(\frac{886}{1665}\right)$	$e\left(\frac{392}{1665}\right)$	$e\left(\frac{343}{3330}\right)$
$\chi_{61969}(14,\cdot)$	61969.gg	3330	yes	$-1$	$1$	$e\left(\frac{428}{555}\right)$	$e\left(\frac{1307}{3330}\right)$	$e\left(\frac{301}{555}\right)$	$e\left(\frac{146}{333}\right)$	$e\left(\frac{109}{666}\right)$	$e\left(\frac{527}{1110}\right)$	$e\left(\frac{58}{185}\right)$	$e\left(\frac{1307}{1665}\right)$	$e\left(\frac{349}{1665}\right)$	$e\left(\frac{673}{1665}\right)$
$\chi_{61969}(15,\cdot)$	61969.gs	9990	yes	$1$	$1$	$e\left(\frac{802}{1665}\right)$	$e\left(\frac{134}{4995}\right)$	$e\left(\frac{1604}{1665}\right)$	$e\left(\frac{91}{999}\right)$	$e\left(\frac{508}{999}\right)$	$e\left(\frac{1163}{3330}\right)$	$e\left(\frac{247}{555}\right)$	$e\left(\frac{268}{4995}\right)$	$e\left(\frac{2861}{4995}\right)$	$e\left(\frac{1879}{9990}\right)$
$\chi_{61969}(16,\cdot)$	61969.fn	1665	yes	$1$	$1$	$e\left(\frac{289}{555}\right)$	$e\left(\frac{368}{1665}\right)$	$e\left(\frac{23}{555}\right)$	$e\left(\frac{235}{333}\right)$	$e\left(\frac{247}{333}\right)$	$e\left(\frac{313}{555}\right)$	$e\left(\frac{104}{185}\right)$	$e\left(\frac{736}{1665}\right)$	$e\left(\frac{377}{1665}\right)$	$e\left(\frac{269}{1665}\right)$
$\chi_{61969}(17,\cdot)$	61969.gl	9990	yes	$1$	$1$	$e\left(\frac{4}{1665}\right)$	$e\left(\frac{4568}{4995}\right)$	$e\left(\frac{8}{1665}\right)$	$e\left(\frac{796}{999}\right)$	$e\left(\frac{916}{999}\right)$	$e\left(\frac{821}{3330}\right)$	$e\left(\frac{4}{555}\right)$	$e\left(\frac{4141}{4995}\right)$	$e\left(\frac{3992}{4995}\right)$	$e\left(\frac{3493}{9990}\right)$
$\chi_{61969}(18,\cdot)$	61969.gj	4995	yes	$1$	$1$	$e\left(\frac{817}{1665}\right)$	$e\left(\frac{614}{4995}\right)$	$e\left(\frac{1634}{1665}\right)$	$e\left(\frac{412}{999}\right)$	$e\left(\frac{613}{999}\right)$	$e\left(\frac{109}{1665}\right)$	$e\left(\frac{262}{555}\right)$	$e\left(\frac{1228}{4995}\right)$	$e\left(\frac{4511}{4995}\right)$	$e\left(\frac{1037}{4995}\right)$
$\chi_{61969}(19,\cdot)$	61969.gr	9990	yes	$-1$	$1$	$e\left(\frac{1478}{1665}\right)$	$e\left(\frac{4127}{9990}\right)$	$e\left(\frac{1291}{1665}\right)$	$e\left(\frac{83}{999}\right)$	$e\left(\frac{601}{1998}\right)$	$e\left(\frac{1717}{3330}\right)$	$e\left(\frac{368}{555}\right)$	$e\left(\frac{4127}{4995}\right)$	$e\left(\frac{4849}{4995}\right)$	$e\left(\frac{3058}{4995}\right)$
$\chi_{61969}(20,\cdot)$	61969.gk	4995	yes	$1$	$1$	$e\left(\frac{311}{1665}\right)$	$e\left(\frac{517}{4995}\right)$	$e\left(\frac{622}{1665}\right)$	$e\left(\frac{950}{999}\right)$	$e\left(\frac{290}{999}\right)$	$e\left(\frac{1322}{1665}\right)$	$e\left(\frac{311}{555}\right)$	$e\left(\frac{1034}{4995}\right)$	$e\left(\frac{688}{4995}\right)$	$e\left(\frac{301}{4995}\right)$
$\chi_{61969}(21,\cdot)$	61969.gt	9990	yes	$-1$	$1$	$e\left(\frac{743}{1665}\right)$	$e\left(\frac{3707}{9990}\right)$	$e\left(\frac{1486}{1665}\right)$	$e\left(\frac{5}{999}\right)$	$e\left(\frac{1633}{1998}\right)$	$e\left(\frac{701}{1665}\right)$	$e\left(\frac{188}{555}\right)$	$e\left(\frac{3707}{4995}\right)$	$e\left(\frac{2254}{4995}\right)$	$e\left(\frac{3221}{9990}\right)$
$\chi_{61969}(22,\cdot)$	61969.gt	9990	yes	$-1$	$1$	$e\left(\frac{284}{1665}\right)$	$e\left(\frac{7631}{9990}\right)$	$e\left(\frac{568}{1665}\right)$	$e\left(\frac{905}{999}\right)$	$e\left(\frac{1867}{1998}\right)$	$e\left(\frac{8}{1665}\right)$	$e\left(\frac{284}{555}\right)$	$e\left(\frac{2636}{4995}\right)$	$e\left(\frac{382}{4995}\right)$	$e\left(\frac{1583}{9990}\right)$
$\chi_{61969}(23,\cdot)$	61969.go	9990	yes	$-1$	$1$	$e\left(\frac{869}{1665}\right)$	$e\left(\frac{8441}{9990}\right)$	$e\left(\frac{73}{1665}\right)$	$e\left(\frac{104}{999}\right)$	$e\left(\frac{733}{1998}\right)$	$e\left(\frac{1283}{1665}\right)$	$e\left(\frac{314}{555}\right)$	$e\left(\frac{3446}{4995}\right)$	$e\left(\frac{3127}{4995}\right)$	$e\left(\frac{863}{9990}\right)$
$\chi_{61969}(24,\cdot)$	61969.gq	9990	yes	$1$	$1$	$e\left(\frac{326}{1665}\right)$	$e\left(\frac{997}{4995}\right)$	$e\left(\frac{652}{1665}\right)$	$e\left(\frac{272}{999}\right)$	$e\left(\frac{395}{999}\right)$	$e\left(\frac{1699}{3330}\right)$	$e\left(\frac{326}{555}\right)$	$e\left(\frac{1994}{4995}\right)$	$e\left(\frac{2338}{4995}\right)$	$e\left(\frac{797}{9990}\right)$
$\chi_{61969}(25,\cdot)$	61969.ey	999	yes	$1$	$1$	$e\left(\frac{284}{333}\right)$	$e\left(\frac{985}{999}\right)$	$e\left(\frac{235}{333}\right)$	$e\left(\frac{196}{999}\right)$	$e\left(\frac{838}{999}\right)$	$e\left(\frac{8}{333}\right)$	$e\left(\frac{62}{111}\right)$	$e\left(\frac{971}{999}\right)$	$e\left(\frac{49}{999}\right)$	$e\left(\frac{958}{999}\right)$
$\chi_{61969}(26,\cdot)$	61969.ep	666	yes	$-1$	$1$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{547}{666}\right)$	$e\left(\frac{83}{111}\right)$	$e\left(\frac{56}{333}\right)$	$e\left(\frac{463}{666}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{214}{333}\right)$	$e\left(\frac{14}{333}\right)$	$e\left(\frac{595}{666}\right)$
$\chi_{61969}(27,\cdot)$	61969.gf	3330	yes	$1$	$1$	$e\left(\frac{92}{555}\right)$	$e\left(\frac{169}{1665}\right)$	$e\left(\frac{184}{555}\right)$	$e\left(\frac{326}{333}\right)$	$e\left(\frac{89}{333}\right)$	$e\left(\frac{13}{1110}\right)$	$e\left(\frac{92}{185}\right)$	$e\left(\frac{338}{1665}\right)$	$e\left(\frac{241}{1665}\right)$	$e\left(\frac{419}{3330}\right)$
$\chi_{61969}(28,\cdot)$	61969.fh	1110	yes	$-1$	$1$	$e\left(\frac{28}{185}\right)$	$e\left(\frac{497}{1110}\right)$	$e\left(\frac{56}{185}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{961}{1110}\right)$	$e\left(\frac{84}{185}\right)$	$e\left(\frac{497}{555}\right)$	$e\left(\frac{3}{185}\right)$	$e\left(\frac{36}{185}\right)$
$\chi_{61969}(29,\cdot)$	61969.gs	9990	yes	$1$	$1$	$e\left(\frac{338}{1665}\right)$	$e\left(\frac{3046}{4995}\right)$	$e\left(\frac{676}{1665}\right)$	$e\left(\frac{995}{999}\right)$	$e\left(\frac{812}{999}\right)$	$e\left(\frac{1387}{3330}\right)$	$e\left(\frac{338}{555}\right)$	$e\left(\frac{1097}{4995}\right)$	$e\left(\frac{994}{4995}\right)$	$e\left(\frac{9611}{9990}\right)$
$\chi_{61969}(30,\cdot)$	61969.fu	1998	yes	$1$	$1$	$e\left(\frac{287}{333}\right)$	$e\left(\frac{82}{999}\right)$	$e\left(\frac{241}{333}\right)$	$e\left(\frac{517}{999}\right)$	$e\left(\frac{943}{999}\right)$	$e\left(\frac{493}{666}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{164}{999}\right)$	$e\left(\frac{379}{999}\right)$	$e\left(\frac{1955}{1998}\right)$
$\chi_{61969}(32,\cdot)$	61969.eh	333	no	$1$	$1$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{92}{333}\right)$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{44}{333}\right)$	$e\left(\frac{59}{333}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{184}{333}\right)$	$e\left(\frac{11}{333}\right)$	$e\left(\frac{317}{333}\right)$
$\chi_{61969}(33,\cdot)$	61969.gp	9990	yes	$-1$	$1$	$e\left(\frac{1408}{1665}\right)$	$e\left(\frac{7417}{9990}\right)$	$e\left(\frac{1151}{1665}\right)$	$e\left(\frac{472}{999}\right)$	$e\left(\frac{1175}{1998}\right)$	$e\left(\frac{3167}{3330}\right)$	$e\left(\frac{298}{555}\right)$	$e\left(\frac{2422}{4995}\right)$	$e\left(\frac{1589}{4995}\right)$	$e\left(\frac{383}{4995}\right)$

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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	$61969$
Structure	\(C_{6}\times C_{9990}\)
Order	$59940$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{61969}(1,\cdot)\)	61969.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{61969}(2,\cdot)\)	61969.fn	1665	yes	\(1\)	\(1\)	\(e\left(\frac{211}{555}\right)\)	\(e\left(\frac{92}{1665}\right)\)	\(e\left(\frac{422}{555}\right)\)	\(e\left(\frac{142}{333}\right)\)	\(e\left(\frac{145}{333}\right)\)	\(e\left(\frac{217}{555}\right)\)	\(e\left(\frac{26}{185}\right)\)	\(e\left(\frac{184}{1665}\right)\)	\(e\left(\frac{1343}{1665}\right)\)	\(e\left(\frac{1316}{1665}\right)\)
\(\chi_{61969}(3,\cdot)\)	61969.gq	9990	yes	\(1\)	\(1\)	\(e\left(\frac{92}{1665}\right)\)	\(e\left(\frac{169}{4995}\right)\)	\(e\left(\frac{184}{1665}\right)\)	\(e\left(\frac{992}{999}\right)\)	\(e\left(\frac{89}{999}\right)\)	\(e\left(\frac{1123}{3330}\right)\)	\(e\left(\frac{92}{555}\right)\)	\(e\left(\frac{338}{4995}\right)\)	\(e\left(\frac{241}{4995}\right)\)	\(e\left(\frac{7079}{9990}\right)\)
\(\chi_{61969}(4,\cdot)\)	61969.fn	1665	yes	\(1\)	\(1\)	\(e\left(\frac{422}{555}\right)\)	\(e\left(\frac{184}{1665}\right)\)	\(e\left(\frac{289}{555}\right)\)	\(e\left(\frac{284}{333}\right)\)	\(e\left(\frac{290}{333}\right)\)	\(e\left(\frac{434}{555}\right)\)	\(e\left(\frac{52}{185}\right)\)	\(e\left(\frac{368}{1665}\right)\)	\(e\left(\frac{1021}{1665}\right)\)	\(e\left(\frac{967}{1665}\right)\)
\(\chi_{61969}(5,\cdot)\)	61969.ey	999	yes	\(1\)	\(1\)	\(e\left(\frac{142}{333}\right)\)	\(e\left(\frac{992}{999}\right)\)	\(e\left(\frac{284}{333}\right)\)	\(e\left(\frac{98}{999}\right)\)	\(e\left(\frac{419}{999}\right)\)	\(e\left(\frac{4}{333}\right)\)	\(e\left(\frac{31}{111}\right)\)	\(e\left(\frac{985}{999}\right)\)	\(e\left(\frac{524}{999}\right)\)	\(e\left(\frac{479}{999}\right)\)
\(\chi_{61969}(6,\cdot)\)	61969.fs	1998	yes	\(1\)	\(1\)	\(e\left(\frac{145}{333}\right)\)	\(e\left(\frac{89}{999}\right)\)	\(e\left(\frac{290}{333}\right)\)	\(e\left(\frac{419}{999}\right)\)	\(e\left(\frac{524}{999}\right)\)	\(e\left(\frac{485}{666}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{178}{999}\right)\)	\(e\left(\frac{854}{999}\right)\)	\(e\left(\frac{997}{1998}\right)\)
\(\chi_{61969}(7,\cdot)\)	61969.fz	3330	yes	\(-1\)	\(1\)	\(e\left(\frac{217}{555}\right)\)	\(e\left(\frac{1123}{3330}\right)\)	\(e\left(\frac{434}{555}\right)\)	\(e\left(\frac{4}{333}\right)\)	\(e\left(\frac{485}{666}\right)\)	\(e\left(\frac{31}{370}\right)\)	\(e\left(\frac{32}{185}\right)\)	\(e\left(\frac{1123}{1665}\right)\)	\(e\left(\frac{671}{1665}\right)\)	\(e\left(\frac{1022}{1665}\right)\)
\(\chi_{61969}(8,\cdot)\)	61969.en	555	yes	\(1\)	\(1\)	\(e\left(\frac{26}{185}\right)\)	\(e\left(\frac{92}{555}\right)\)	\(e\left(\frac{52}{185}\right)\)	\(e\left(\frac{31}{111}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{32}{185}\right)\)	\(e\left(\frac{78}{185}\right)\)	\(e\left(\frac{184}{555}\right)\)	\(e\left(\frac{233}{555}\right)\)	\(e\left(\frac{206}{555}\right)\)
\(\chi_{61969}(9,\cdot)\)	61969.gj	4995	yes	\(1\)	\(1\)	\(e\left(\frac{184}{1665}\right)\)	\(e\left(\frac{338}{4995}\right)\)	\(e\left(\frac{368}{1665}\right)\)	\(e\left(\frac{985}{999}\right)\)	\(e\left(\frac{178}{999}\right)\)	\(e\left(\frac{1123}{1665}\right)\)	\(e\left(\frac{184}{555}\right)\)	\(e\left(\frac{676}{4995}\right)\)	\(e\left(\frac{482}{4995}\right)\)	\(e\left(\frac{2084}{4995}\right)\)
\(\chi_{61969}(10,\cdot)\)	61969.gk	4995	yes	\(1\)	\(1\)	\(e\left(\frac{1343}{1665}\right)\)	\(e\left(\frac{241}{4995}\right)\)	\(e\left(\frac{1021}{1665}\right)\)	\(e\left(\frac{524}{999}\right)\)	\(e\left(\frac{854}{999}\right)\)	\(e\left(\frac{671}{1665}\right)\)	\(e\left(\frac{233}{555}\right)\)	\(e\left(\frac{482}{4995}\right)\)	\(e\left(\frac{1654}{4995}\right)\)	\(e\left(\frac{1348}{4995}\right)\)
\(\chi_{61969}(11,\cdot)\)	61969.gt	9990	yes	\(-1\)	\(1\)	\(e\left(\frac{1316}{1665}\right)\)	\(e\left(\frac{7079}{9990}\right)\)	\(e\left(\frac{967}{1665}\right)\)	\(e\left(\frac{479}{999}\right)\)	\(e\left(\frac{997}{1998}\right)\)	\(e\left(\frac{1022}{1665}\right)\)	\(e\left(\frac{206}{555}\right)\)	\(e\left(\frac{2084}{4995}\right)\)	\(e\left(\frac{1348}{4995}\right)\)	\(e\left(\frac{3677}{9990}\right)\)
\(\chi_{61969}(12,\cdot)\)	61969.gq	9990	yes	\(1\)	\(1\)	\(e\left(\frac{1358}{1665}\right)\)	\(e\left(\frac{721}{4995}\right)\)	\(e\left(\frac{1051}{1665}\right)\)	\(e\left(\frac{845}{999}\right)\)	\(e\left(\frac{959}{999}\right)\)	\(e\left(\frac{397}{3330}\right)\)	\(e\left(\frac{248}{555}\right)\)	\(e\left(\frac{1442}{4995}\right)\)	\(e\left(\frac{3304}{4995}\right)\)	\(e\left(\frac{2891}{9990}\right)\)
\(\chi_{61969}(13,\cdot)\)	61969.gb	3330	yes	\(-1\)	\(1\)	\(e\left(\frac{274}{555}\right)\)	\(e\left(\frac{2551}{3330}\right)\)	\(e\left(\frac{548}{555}\right)\)	\(e\left(\frac{247}{333}\right)\)	\(e\left(\frac{173}{666}\right)\)	\(e\left(\frac{323}{555}\right)\)	\(e\left(\frac{89}{185}\right)\)	\(e\left(\frac{886}{1665}\right)\)	\(e\left(\frac{392}{1665}\right)\)	\(e\left(\frac{343}{3330}\right)\)
\(\chi_{61969}(14,\cdot)\)	61969.gg	3330	yes	\(-1\)	\(1\)	\(e\left(\frac{428}{555}\right)\)	\(e\left(\frac{1307}{3330}\right)\)	\(e\left(\frac{301}{555}\right)\)	\(e\left(\frac{146}{333}\right)\)	\(e\left(\frac{109}{666}\right)\)	\(e\left(\frac{527}{1110}\right)\)	\(e\left(\frac{58}{185}\right)\)	\(e\left(\frac{1307}{1665}\right)\)	\(e\left(\frac{349}{1665}\right)\)	\(e\left(\frac{673}{1665}\right)\)
\(\chi_{61969}(15,\cdot)\)	61969.gs	9990	yes	\(1\)	\(1\)	\(e\left(\frac{802}{1665}\right)\)	\(e\left(\frac{134}{4995}\right)\)	\(e\left(\frac{1604}{1665}\right)\)	\(e\left(\frac{91}{999}\right)\)	\(e\left(\frac{508}{999}\right)\)	\(e\left(\frac{1163}{3330}\right)\)	\(e\left(\frac{247}{555}\right)\)	\(e\left(\frac{268}{4995}\right)\)	\(e\left(\frac{2861}{4995}\right)\)	\(e\left(\frac{1879}{9990}\right)\)
\(\chi_{61969}(16,\cdot)\)	61969.fn	1665	yes	\(1\)	\(1\)	\(e\left(\frac{289}{555}\right)\)	\(e\left(\frac{368}{1665}\right)\)	\(e\left(\frac{23}{555}\right)\)	\(e\left(\frac{235}{333}\right)\)	\(e\left(\frac{247}{333}\right)\)	\(e\left(\frac{313}{555}\right)\)	\(e\left(\frac{104}{185}\right)\)	\(e\left(\frac{736}{1665}\right)\)	\(e\left(\frac{377}{1665}\right)\)	\(e\left(\frac{269}{1665}\right)\)
\(\chi_{61969}(17,\cdot)\)	61969.gl	9990	yes	\(1\)	\(1\)	\(e\left(\frac{4}{1665}\right)\)	\(e\left(\frac{4568}{4995}\right)\)	\(e\left(\frac{8}{1665}\right)\)	\(e\left(\frac{796}{999}\right)\)	\(e\left(\frac{916}{999}\right)\)	\(e\left(\frac{821}{3330}\right)\)	\(e\left(\frac{4}{555}\right)\)	\(e\left(\frac{4141}{4995}\right)\)	\(e\left(\frac{3992}{4995}\right)\)	\(e\left(\frac{3493}{9990}\right)\)
\(\chi_{61969}(18,\cdot)\)	61969.gj	4995	yes	\(1\)	\(1\)	\(e\left(\frac{817}{1665}\right)\)	\(e\left(\frac{614}{4995}\right)\)	\(e\left(\frac{1634}{1665}\right)\)	\(e\left(\frac{412}{999}\right)\)	\(e\left(\frac{613}{999}\right)\)	\(e\left(\frac{109}{1665}\right)\)	\(e\left(\frac{262}{555}\right)\)	\(e\left(\frac{1228}{4995}\right)\)	\(e\left(\frac{4511}{4995}\right)\)	\(e\left(\frac{1037}{4995}\right)\)
\(\chi_{61969}(19,\cdot)\)	61969.gr	9990	yes	\(-1\)	\(1\)	\(e\left(\frac{1478}{1665}\right)\)	\(e\left(\frac{4127}{9990}\right)\)	\(e\left(\frac{1291}{1665}\right)\)	\(e\left(\frac{83}{999}\right)\)	\(e\left(\frac{601}{1998}\right)\)	\(e\left(\frac{1717}{3330}\right)\)	\(e\left(\frac{368}{555}\right)\)	\(e\left(\frac{4127}{4995}\right)\)	\(e\left(\frac{4849}{4995}\right)\)	\(e\left(\frac{3058}{4995}\right)\)
\(\chi_{61969}(20,\cdot)\)	61969.gk	4995	yes	\(1\)	\(1\)	\(e\left(\frac{311}{1665}\right)\)	\(e\left(\frac{517}{4995}\right)\)	\(e\left(\frac{622}{1665}\right)\)	\(e\left(\frac{950}{999}\right)\)	\(e\left(\frac{290}{999}\right)\)	\(e\left(\frac{1322}{1665}\right)\)	\(e\left(\frac{311}{555}\right)\)	\(e\left(\frac{1034}{4995}\right)\)	\(e\left(\frac{688}{4995}\right)\)	\(e\left(\frac{301}{4995}\right)\)
\(\chi_{61969}(21,\cdot)\)	61969.gt	9990	yes	\(-1\)	\(1\)	\(e\left(\frac{743}{1665}\right)\)	\(e\left(\frac{3707}{9990}\right)\)	\(e\left(\frac{1486}{1665}\right)\)	\(e\left(\frac{5}{999}\right)\)	\(e\left(\frac{1633}{1998}\right)\)	\(e\left(\frac{701}{1665}\right)\)	\(e\left(\frac{188}{555}\right)\)	\(e\left(\frac{3707}{4995}\right)\)	\(e\left(\frac{2254}{4995}\right)\)	\(e\left(\frac{3221}{9990}\right)\)
\(\chi_{61969}(22,\cdot)\)	61969.gt	9990	yes	\(-1\)	\(1\)	\(e\left(\frac{284}{1665}\right)\)	\(e\left(\frac{7631}{9990}\right)\)	\(e\left(\frac{568}{1665}\right)\)	\(e\left(\frac{905}{999}\right)\)	\(e\left(\frac{1867}{1998}\right)\)	\(e\left(\frac{8}{1665}\right)\)	\(e\left(\frac{284}{555}\right)\)	\(e\left(\frac{2636}{4995}\right)\)	\(e\left(\frac{382}{4995}\right)\)	\(e\left(\frac{1583}{9990}\right)\)
\(\chi_{61969}(23,\cdot)\)	61969.go	9990	yes	\(-1\)	\(1\)	\(e\left(\frac{869}{1665}\right)\)	\(e\left(\frac{8441}{9990}\right)\)	\(e\left(\frac{73}{1665}\right)\)	\(e\left(\frac{104}{999}\right)\)	\(e\left(\frac{733}{1998}\right)\)	\(e\left(\frac{1283}{1665}\right)\)	\(e\left(\frac{314}{555}\right)\)	\(e\left(\frac{3446}{4995}\right)\)	\(e\left(\frac{3127}{4995}\right)\)	\(e\left(\frac{863}{9990}\right)\)
\(\chi_{61969}(24,\cdot)\)	61969.gq	9990	yes	\(1\)	\(1\)	\(e\left(\frac{326}{1665}\right)\)	\(e\left(\frac{997}{4995}\right)\)	\(e\left(\frac{652}{1665}\right)\)	\(e\left(\frac{272}{999}\right)\)	\(e\left(\frac{395}{999}\right)\)	\(e\left(\frac{1699}{3330}\right)\)	\(e\left(\frac{326}{555}\right)\)	\(e\left(\frac{1994}{4995}\right)\)	\(e\left(\frac{2338}{4995}\right)\)	\(e\left(\frac{797}{9990}\right)\)
\(\chi_{61969}(25,\cdot)\)	61969.ey	999	yes	\(1\)	\(1\)	\(e\left(\frac{284}{333}\right)\)	\(e\left(\frac{985}{999}\right)\)	\(e\left(\frac{235}{333}\right)\)	\(e\left(\frac{196}{999}\right)\)	\(e\left(\frac{838}{999}\right)\)	\(e\left(\frac{8}{333}\right)\)	\(e\left(\frac{62}{111}\right)\)	\(e\left(\frac{971}{999}\right)\)	\(e\left(\frac{49}{999}\right)\)	\(e\left(\frac{958}{999}\right)\)
\(\chi_{61969}(26,\cdot)\)	61969.ep	666	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{547}{666}\right)\)	\(e\left(\frac{83}{111}\right)\)	\(e\left(\frac{56}{333}\right)\)	\(e\left(\frac{463}{666}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{214}{333}\right)\)	\(e\left(\frac{14}{333}\right)\)	\(e\left(\frac{595}{666}\right)\)
\(\chi_{61969}(27,\cdot)\)	61969.gf	3330	yes	\(1\)	\(1\)	\(e\left(\frac{92}{555}\right)\)	\(e\left(\frac{169}{1665}\right)\)	\(e\left(\frac{184}{555}\right)\)	\(e\left(\frac{326}{333}\right)\)	\(e\left(\frac{89}{333}\right)\)	\(e\left(\frac{13}{1110}\right)\)	\(e\left(\frac{92}{185}\right)\)	\(e\left(\frac{338}{1665}\right)\)	\(e\left(\frac{241}{1665}\right)\)	\(e\left(\frac{419}{3330}\right)\)
\(\chi_{61969}(28,\cdot)\)	61969.fh	1110	yes	\(-1\)	\(1\)	\(e\left(\frac{28}{185}\right)\)	\(e\left(\frac{497}{1110}\right)\)	\(e\left(\frac{56}{185}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{961}{1110}\right)\)	\(e\left(\frac{84}{185}\right)\)	\(e\left(\frac{497}{555}\right)\)	\(e\left(\frac{3}{185}\right)\)	\(e\left(\frac{36}{185}\right)\)
\(\chi_{61969}(29,\cdot)\)	61969.gs	9990	yes	\(1\)	\(1\)	\(e\left(\frac{338}{1665}\right)\)	\(e\left(\frac{3046}{4995}\right)\)	\(e\left(\frac{676}{1665}\right)\)	\(e\left(\frac{995}{999}\right)\)	\(e\left(\frac{812}{999}\right)\)	\(e\left(\frac{1387}{3330}\right)\)	\(e\left(\frac{338}{555}\right)\)	\(e\left(\frac{1097}{4995}\right)\)	\(e\left(\frac{994}{4995}\right)\)	\(e\left(\frac{9611}{9990}\right)\)
\(\chi_{61969}(30,\cdot)\)	61969.fu	1998	yes	\(1\)	\(1\)	\(e\left(\frac{287}{333}\right)\)	\(e\left(\frac{82}{999}\right)\)	\(e\left(\frac{241}{333}\right)\)	\(e\left(\frac{517}{999}\right)\)	\(e\left(\frac{943}{999}\right)\)	\(e\left(\frac{493}{666}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{164}{999}\right)\)	\(e\left(\frac{379}{999}\right)\)	\(e\left(\frac{1955}{1998}\right)\)
\(\chi_{61969}(32,\cdot)\)	61969.eh	333	no	\(1\)	\(1\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{92}{333}\right)\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{44}{333}\right)\)	\(e\left(\frac{59}{333}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{184}{333}\right)\)	\(e\left(\frac{11}{333}\right)\)	\(e\left(\frac{317}{333}\right)\)
\(\chi_{61969}(33,\cdot)\)	61969.gp	9990	yes	\(-1\)	\(1\)	\(e\left(\frac{1408}{1665}\right)\)	\(e\left(\frac{7417}{9990}\right)\)	\(e\left(\frac{1151}{1665}\right)\)	\(e\left(\frac{472}{999}\right)\)	\(e\left(\frac{1175}{1998}\right)\)	\(e\left(\frac{3167}{3330}\right)\)	\(e\left(\frac{298}{555}\right)\)	\(e\left(\frac{2422}{4995}\right)\)	\(e\left(\frac{1589}{4995}\right)\)	\(e\left(\frac{383}{4995}\right)\)

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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.