LMFDB - Group of Dirichlet characters of modulus 8013

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8013)

pari: g = idealstar(,8013,2)

Character group

sage: G.order() pari: g.no
Order	=	5340
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2670}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8013}(2672,\cdot)$, $\chi_{8013}(7,\cdot)$

First 32 of 5340 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8013}(1,\cdot)$	8013.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8013}(2,\cdot)$	8013.ba	890	yes	$-1$	$1$	$e\left(\frac{867}{890}\right)$	$e\left(\frac{422}{445}\right)$	$e\left(\frac{589}{890}\right)$	$e\left(\frac{36}{445}\right)$	$e\left(\frac{821}{890}\right)$	$e\left(\frac{283}{445}\right)$	$e\left(\frac{737}{890}\right)$	$e\left(\frac{147}{445}\right)$	$e\left(\frac{49}{890}\right)$	$e\left(\frac{399}{445}\right)$
$\chi_{8013}(4,\cdot)$	8013.v	445	no	$1$	$1$	$e\left(\frac{422}{445}\right)$	$e\left(\frac{399}{445}\right)$	$e\left(\frac{144}{445}\right)$	$e\left(\frac{72}{445}\right)$	$e\left(\frac{376}{445}\right)$	$e\left(\frac{121}{445}\right)$	$e\left(\frac{292}{445}\right)$	$e\left(\frac{294}{445}\right)$	$e\left(\frac{49}{445}\right)$	$e\left(\frac{353}{445}\right)$
$\chi_{8013}(5,\cdot)$	8013.bd	2670	yes	$-1$	$1$	$e\left(\frac{589}{890}\right)$	$e\left(\frac{144}{445}\right)$	$e\left(\frac{1339}{2670}\right)$	$e\left(\frac{446}{1335}\right)$	$e\left(\frac{877}{890}\right)$	$e\left(\frac{218}{1335}\right)$	$e\left(\frac{629}{890}\right)$	$e\left(\frac{434}{445}\right)$	$e\left(\frac{2659}{2670}\right)$	$e\left(\frac{288}{445}\right)$
$\chi_{8013}(7,\cdot)$	8013.bf	2670	no	$-1$	$1$	$e\left(\frac{36}{445}\right)$	$e\left(\frac{72}{445}\right)$	$e\left(\frac{446}{1335}\right)$	$e\left(\frac{1}{2670}\right)$	$e\left(\frac{108}{445}\right)$	$e\left(\frac{554}{1335}\right)$	$e\left(\frac{537}{890}\right)$	$e\left(\frac{879}{890}\right)$	$e\left(\frac{217}{2670}\right)$	$e\left(\frac{144}{445}\right)$
$\chi_{8013}(8,\cdot)$	8013.ba	890	yes	$-1$	$1$	$e\left(\frac{821}{890}\right)$	$e\left(\frac{376}{445}\right)$	$e\left(\frac{877}{890}\right)$	$e\left(\frac{108}{445}\right)$	$e\left(\frac{683}{890}\right)$	$e\left(\frac{404}{445}\right)$	$e\left(\frac{431}{890}\right)$	$e\left(\frac{441}{445}\right)$	$e\left(\frac{147}{890}\right)$	$e\left(\frac{307}{445}\right)$
$\chi_{8013}(10,\cdot)$	8013.bc	1335	no	$1$	$1$	$e\left(\frac{283}{445}\right)$	$e\left(\frac{121}{445}\right)$	$e\left(\frac{218}{1335}\right)$	$e\left(\frac{554}{1335}\right)$	$e\left(\frac{404}{445}\right)$	$e\left(\frac{1067}{1335}\right)$	$e\left(\frac{238}{445}\right)$	$e\left(\frac{136}{445}\right)$	$e\left(\frac{68}{1335}\right)$	$e\left(\frac{242}{445}\right)$
$\chi_{8013}(11,\cdot)$	8013.z	890	yes	$1$	$1$	$e\left(\frac{737}{890}\right)$	$e\left(\frac{292}{445}\right)$	$e\left(\frac{629}{890}\right)$	$e\left(\frac{537}{890}\right)$	$e\left(\frac{431}{890}\right)$	$e\left(\frac{238}{445}\right)$	$e\left(\frac{236}{445}\right)$	$e\left(\frac{79}{890}\right)$	$e\left(\frac{192}{445}\right)$	$e\left(\frac{139}{445}\right)$
$\chi_{8013}(13,\cdot)$	8013.bb	890	no	$-1$	$1$	$e\left(\frac{147}{445}\right)$	$e\left(\frac{294}{445}\right)$	$e\left(\frac{434}{445}\right)$	$e\left(\frac{879}{890}\right)$	$e\left(\frac{441}{445}\right)$	$e\left(\frac{136}{445}\right)$	$e\left(\frac{79}{890}\right)$	$e\left(\frac{363}{890}\right)$	$e\left(\frac{283}{890}\right)$	$e\left(\frac{143}{445}\right)$
$\chi_{8013}(14,\cdot)$	8013.be	2670	yes	$1$	$1$	$e\left(\frac{49}{890}\right)$	$e\left(\frac{49}{445}\right)$	$e\left(\frac{2659}{2670}\right)$	$e\left(\frac{217}{2670}\right)$	$e\left(\frac{147}{890}\right)$	$e\left(\frac{68}{1335}\right)$	$e\left(\frac{192}{445}\right)$	$e\left(\frac{283}{890}\right)$	$e\left(\frac{182}{1335}\right)$	$e\left(\frac{98}{445}\right)$
$\chi_{8013}(16,\cdot)$	8013.v	445	no	$1$	$1$	$e\left(\frac{399}{445}\right)$	$e\left(\frac{353}{445}\right)$	$e\left(\frac{288}{445}\right)$	$e\left(\frac{144}{445}\right)$	$e\left(\frac{307}{445}\right)$	$e\left(\frac{242}{445}\right)$	$e\left(\frac{139}{445}\right)$	$e\left(\frac{143}{445}\right)$	$e\left(\frac{98}{445}\right)$	$e\left(\frac{261}{445}\right)$
$\chi_{8013}(17,\cdot)$	8013.y	534	yes	$-1$	$1$	$e\left(\frac{23}{178}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{191}{534}\right)$	$e\left(\frac{70}{267}\right)$	$e\left(\frac{69}{178}\right)$	$e\left(\frac{130}{267}\right)$	$e\left(\frac{153}{178}\right)$	$e\left(\frac{31}{89}\right)$	$e\left(\frac{209}{534}\right)$	$e\left(\frac{46}{89}\right)$
$\chi_{8013}(19,\cdot)$	8013.bf	2670	no	$-1$	$1$	$e\left(\frac{61}{445}\right)$	$e\left(\frac{122}{445}\right)$	$e\left(\frac{731}{1335}\right)$	$e\left(\frac{1621}{2670}\right)$	$e\left(\frac{183}{445}\right)$	$e\left(\frac{914}{1335}\right)$	$e\left(\frac{57}{890}\right)$	$e\left(\frac{859}{890}\right)$	$e\left(\frac{1987}{2670}\right)$	$e\left(\frac{244}{445}\right)$
$\chi_{8013}(20,\cdot)$	8013.bd	2670	yes	$-1$	$1$	$e\left(\frac{543}{890}\right)$	$e\left(\frac{98}{445}\right)$	$e\left(\frac{2203}{2670}\right)$	$e\left(\frac{662}{1335}\right)$	$e\left(\frac{739}{890}\right)$	$e\left(\frac{581}{1335}\right)$	$e\left(\frac{323}{890}\right)$	$e\left(\frac{283}{445}\right)$	$e\left(\frac{283}{2670}\right)$	$e\left(\frac{196}{445}\right)$
$\chi_{8013}(22,\cdot)$	8013.bb	890	no	$-1$	$1$	$e\left(\frac{357}{445}\right)$	$e\left(\frac{269}{445}\right)$	$e\left(\frac{164}{445}\right)$	$e\left(\frac{609}{890}\right)$	$e\left(\frac{181}{445}\right)$	$e\left(\frac{76}{445}\right)$	$e\left(\frac{319}{890}\right)$	$e\left(\frac{373}{890}\right)$	$e\left(\frac{433}{890}\right)$	$e\left(\frac{93}{445}\right)$
$\chi_{8013}(23,\cdot)$	8013.be	2670	yes	$1$	$1$	$e\left(\frac{731}{890}\right)$	$e\left(\frac{286}{445}\right)$	$e\left(\frac{181}{2670}\right)$	$e\left(\frac{313}{2670}\right)$	$e\left(\frac{413}{890}\right)$	$e\left(\frac{1187}{1335}\right)$	$e\left(\frac{158}{445}\right)$	$e\left(\frac{117}{890}\right)$	$e\left(\frac{1253}{1335}\right)$	$e\left(\frac{127}{445}\right)$
$\chi_{8013}(25,\cdot)$	8013.bc	1335	no	$1$	$1$	$e\left(\frac{144}{445}\right)$	$e\left(\frac{288}{445}\right)$	$e\left(\frac{4}{1335}\right)$	$e\left(\frac{892}{1335}\right)$	$e\left(\frac{432}{445}\right)$	$e\left(\frac{436}{1335}\right)$	$e\left(\frac{184}{445}\right)$	$e\left(\frac{423}{445}\right)$	$e\left(\frac{1324}{1335}\right)$	$e\left(\frac{131}{445}\right)$
$\chi_{8013}(26,\cdot)$	8013.z	890	yes	$1$	$1$	$e\left(\frac{271}{890}\right)$	$e\left(\frac{271}{445}\right)$	$e\left(\frac{567}{890}\right)$	$e\left(\frac{61}{890}\right)$	$e\left(\frac{813}{890}\right)$	$e\left(\frac{419}{445}\right)$	$e\left(\frac{408}{445}\right)$	$e\left(\frac{657}{890}\right)$	$e\left(\frac{166}{445}\right)$	$e\left(\frac{97}{445}\right)$
$\chi_{8013}(28,\cdot)$	8013.bf	2670	no	$-1$	$1$	$e\left(\frac{13}{445}\right)$	$e\left(\frac{26}{445}\right)$	$e\left(\frac{878}{1335}\right)$	$e\left(\frac{433}{2670}\right)$	$e\left(\frac{39}{445}\right)$	$e\left(\frac{917}{1335}\right)$	$e\left(\frac{231}{890}\right)$	$e\left(\frac{577}{890}\right)$	$e\left(\frac{511}{2670}\right)$	$e\left(\frac{52}{445}\right)$
$\chi_{8013}(29,\cdot)$	8013.be	2670	yes	$1$	$1$	$e\left(\frac{409}{890}\right)$	$e\left(\frac{409}{445}\right)$	$e\left(\frac{2669}{2670}\right)$	$e\left(\frac{2447}{2670}\right)$	$e\left(\frac{337}{890}\right)$	$e\left(\frac{613}{1335}\right)$	$e\left(\frac{422}{445}\right)$	$e\left(\frac{673}{890}\right)$	$e\left(\frac{502}{1335}\right)$	$e\left(\frac{373}{445}\right)$
$\chi_{8013}(31,\cdot)$	8013.bf	2670	no	$-1$	$1$	$e\left(\frac{274}{445}\right)$	$e\left(\frac{103}{445}\right)$	$e\left(\frac{329}{1335}\right)$	$e\left(\frac{1219}{2670}\right)$	$e\left(\frac{377}{445}\right)$	$e\left(\frac{1151}{1335}\right)$	$e\left(\frac{453}{890}\right)$	$e\left(\frac{831}{890}\right)$	$e\left(\frac{193}{2670}\right)$	$e\left(\frac{206}{445}\right)$
$\chi_{8013}(32,\cdot)$	8013.s	178	yes	$-1$	$1$	$e\left(\frac{155}{178}\right)$	$e\left(\frac{66}{89}\right)$	$e\left(\frac{55}{178}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{109}{178}\right)$	$e\left(\frac{16}{89}\right)$	$e\left(\frac{25}{178}\right)$	$e\left(\frac{58}{89}\right)$	$e\left(\frac{49}{178}\right)$	$e\left(\frac{43}{89}\right)$
$\chi_{8013}(34,\cdot)$	8013.bc	1335	no	$1$	$1$	$e\left(\frac{46}{445}\right)$	$e\left(\frac{92}{445}\right)$	$e\left(\frac{26}{1335}\right)$	$e\left(\frac{458}{1335}\right)$	$e\left(\frac{138}{445}\right)$	$e\left(\frac{164}{1335}\right)$	$e\left(\frac{306}{445}\right)$	$e\left(\frac{302}{445}\right)$	$e\left(\frac{596}{1335}\right)$	$e\left(\frac{184}{445}\right)$
$\chi_{8013}(35,\cdot)$	8013.be	2670	yes	$1$	$1$	$e\left(\frac{661}{890}\right)$	$e\left(\frac{216}{445}\right)$	$e\left(\frac{2231}{2670}\right)$	$e\left(\frac{893}{2670}\right)$	$e\left(\frac{203}{890}\right)$	$e\left(\frac{772}{1335}\right)$	$e\left(\frac{138}{445}\right)$	$e\left(\frac{857}{890}\right)$	$e\left(\frac{103}{1335}\right)$	$e\left(\frac{432}{445}\right)$
$\chi_{8013}(37,\cdot)$	8013.m	15	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{8013}(38,\cdot)$	8013.be	2670	yes	$1$	$1$	$e\left(\frac{99}{890}\right)$	$e\left(\frac{99}{445}\right)$	$e\left(\frac{559}{2670}\right)$	$e\left(\frac{1837}{2670}\right)$	$e\left(\frac{297}{890}\right)$	$e\left(\frac{428}{1335}\right)$	$e\left(\frac{397}{445}\right)$	$e\left(\frac{263}{890}\right)$	$e\left(\frac{1067}{1335}\right)$	$e\left(\frac{198}{445}\right)$
$\chi_{8013}(40,\cdot)$	8013.u	267	no	$1$	$1$	$e\left(\frac{52}{89}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{130}{267}\right)$	$e\left(\frac{154}{267}\right)$	$e\left(\frac{67}{89}\right)$	$e\left(\frac{19}{267}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{43}{267}\right)$	$e\left(\frac{30}{89}\right)$
$\chi_{8013}(41,\cdot)$	8013.be	2670	yes	$1$	$1$	$e\left(\frac{633}{890}\right)$	$e\left(\frac{188}{445}\right)$	$e\left(\frac{203}{2670}\right)$	$e\left(\frac{2549}{2670}\right)$	$e\left(\frac{119}{890}\right)$	$e\left(\frac{1051}{1335}\right)$	$e\left(\frac{219}{445}\right)$	$e\left(\frac{441}{890}\right)$	$e\left(\frac{889}{1335}\right)$	$e\left(\frac{376}{445}\right)$
$\chi_{8013}(43,\cdot)$	8013.v	445	no	$1$	$1$	$e\left(\frac{32}{445}\right)$	$e\left(\frac{64}{445}\right)$	$e\left(\frac{264}{445}\right)$	$e\left(\frac{132}{445}\right)$	$e\left(\frac{96}{445}\right)$	$e\left(\frac{296}{445}\right)$	$e\left(\frac{387}{445}\right)$	$e\left(\frac{94}{445}\right)$	$e\left(\frac{164}{445}\right)$	$e\left(\frac{128}{445}\right)$
$\chi_{8013}(44,\cdot)$	8013.z	890	yes	$1$	$1$	$e\left(\frac{691}{890}\right)$	$e\left(\frac{246}{445}\right)$	$e\left(\frac{27}{890}\right)$	$e\left(\frac{681}{890}\right)$	$e\left(\frac{293}{890}\right)$	$e\left(\frac{359}{445}\right)$	$e\left(\frac{83}{445}\right)$	$e\left(\frac{667}{890}\right)$	$e\left(\frac{241}{445}\right)$	$e\left(\frac{47}{445}\right)$
$\chi_{8013}(46,\cdot)$	8013.bf	2670	no	$-1$	$1$	$e\left(\frac{354}{445}\right)$	$e\left(\frac{263}{445}\right)$	$e\left(\frac{974}{1335}\right)$	$e\left(\frac{529}{2670}\right)$	$e\left(\frac{172}{445}\right)$	$e\left(\frac{701}{1335}\right)$	$e\left(\frac{163}{890}\right)$	$e\left(\frac{411}{890}\right)$	$e\left(\frac{2653}{2670}\right)$	$e\left(\frac{81}{445}\right)$
$\chi_{8013}(47,\cdot)$	8013.y	534	yes	$-1$	$1$	$e\left(\frac{99}{178}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{25}{534}\right)$	$e\left(\frac{251}{267}\right)$	$e\left(\frac{119}{178}\right)$	$e\left(\frac{161}{267}\right)$	$e\left(\frac{171}{178}\right)$	$e\left(\frac{87}{89}\right)$	$e\left(\frac{265}{534}\right)$	$e\left(\frac{20}{89}\right)$

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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	$8013$
Structure	\(C_{2}\times C_{2670}\)
Order	$5340$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8013}(1,\cdot)\)	8013.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8013}(2,\cdot)\)	8013.ba	890	yes	\(-1\)	\(1\)	\(e\left(\frac{867}{890}\right)\)	\(e\left(\frac{422}{445}\right)\)	\(e\left(\frac{589}{890}\right)\)	\(e\left(\frac{36}{445}\right)\)	\(e\left(\frac{821}{890}\right)\)	\(e\left(\frac{283}{445}\right)\)	\(e\left(\frac{737}{890}\right)\)	\(e\left(\frac{147}{445}\right)\)	\(e\left(\frac{49}{890}\right)\)	\(e\left(\frac{399}{445}\right)\)
\(\chi_{8013}(4,\cdot)\)	8013.v	445	no	\(1\)	\(1\)	\(e\left(\frac{422}{445}\right)\)	\(e\left(\frac{399}{445}\right)\)	\(e\left(\frac{144}{445}\right)\)	\(e\left(\frac{72}{445}\right)\)	\(e\left(\frac{376}{445}\right)\)	\(e\left(\frac{121}{445}\right)\)	\(e\left(\frac{292}{445}\right)\)	\(e\left(\frac{294}{445}\right)\)	\(e\left(\frac{49}{445}\right)\)	\(e\left(\frac{353}{445}\right)\)
\(\chi_{8013}(5,\cdot)\)	8013.bd	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{589}{890}\right)\)	\(e\left(\frac{144}{445}\right)\)	\(e\left(\frac{1339}{2670}\right)\)	\(e\left(\frac{446}{1335}\right)\)	\(e\left(\frac{877}{890}\right)\)	\(e\left(\frac{218}{1335}\right)\)	\(e\left(\frac{629}{890}\right)\)	\(e\left(\frac{434}{445}\right)\)	\(e\left(\frac{2659}{2670}\right)\)	\(e\left(\frac{288}{445}\right)\)
\(\chi_{8013}(7,\cdot)\)	8013.bf	2670	no	\(-1\)	\(1\)	\(e\left(\frac{36}{445}\right)\)	\(e\left(\frac{72}{445}\right)\)	\(e\left(\frac{446}{1335}\right)\)	\(e\left(\frac{1}{2670}\right)\)	\(e\left(\frac{108}{445}\right)\)	\(e\left(\frac{554}{1335}\right)\)	\(e\left(\frac{537}{890}\right)\)	\(e\left(\frac{879}{890}\right)\)	\(e\left(\frac{217}{2670}\right)\)	\(e\left(\frac{144}{445}\right)\)
\(\chi_{8013}(8,\cdot)\)	8013.ba	890	yes	\(-1\)	\(1\)	\(e\left(\frac{821}{890}\right)\)	\(e\left(\frac{376}{445}\right)\)	\(e\left(\frac{877}{890}\right)\)	\(e\left(\frac{108}{445}\right)\)	\(e\left(\frac{683}{890}\right)\)	\(e\left(\frac{404}{445}\right)\)	\(e\left(\frac{431}{890}\right)\)	\(e\left(\frac{441}{445}\right)\)	\(e\left(\frac{147}{890}\right)\)	\(e\left(\frac{307}{445}\right)\)
\(\chi_{8013}(10,\cdot)\)	8013.bc	1335	no	\(1\)	\(1\)	\(e\left(\frac{283}{445}\right)\)	\(e\left(\frac{121}{445}\right)\)	\(e\left(\frac{218}{1335}\right)\)	\(e\left(\frac{554}{1335}\right)\)	\(e\left(\frac{404}{445}\right)\)	\(e\left(\frac{1067}{1335}\right)\)	\(e\left(\frac{238}{445}\right)\)	\(e\left(\frac{136}{445}\right)\)	\(e\left(\frac{68}{1335}\right)\)	\(e\left(\frac{242}{445}\right)\)
\(\chi_{8013}(11,\cdot)\)	8013.z	890	yes	\(1\)	\(1\)	\(e\left(\frac{737}{890}\right)\)	\(e\left(\frac{292}{445}\right)\)	\(e\left(\frac{629}{890}\right)\)	\(e\left(\frac{537}{890}\right)\)	\(e\left(\frac{431}{890}\right)\)	\(e\left(\frac{238}{445}\right)\)	\(e\left(\frac{236}{445}\right)\)	\(e\left(\frac{79}{890}\right)\)	\(e\left(\frac{192}{445}\right)\)	\(e\left(\frac{139}{445}\right)\)
\(\chi_{8013}(13,\cdot)\)	8013.bb	890	no	\(-1\)	\(1\)	\(e\left(\frac{147}{445}\right)\)	\(e\left(\frac{294}{445}\right)\)	\(e\left(\frac{434}{445}\right)\)	\(e\left(\frac{879}{890}\right)\)	\(e\left(\frac{441}{445}\right)\)	\(e\left(\frac{136}{445}\right)\)	\(e\left(\frac{79}{890}\right)\)	\(e\left(\frac{363}{890}\right)\)	\(e\left(\frac{283}{890}\right)\)	\(e\left(\frac{143}{445}\right)\)
\(\chi_{8013}(14,\cdot)\)	8013.be	2670	yes	\(1\)	\(1\)	\(e\left(\frac{49}{890}\right)\)	\(e\left(\frac{49}{445}\right)\)	\(e\left(\frac{2659}{2670}\right)\)	\(e\left(\frac{217}{2670}\right)\)	\(e\left(\frac{147}{890}\right)\)	\(e\left(\frac{68}{1335}\right)\)	\(e\left(\frac{192}{445}\right)\)	\(e\left(\frac{283}{890}\right)\)	\(e\left(\frac{182}{1335}\right)\)	\(e\left(\frac{98}{445}\right)\)
\(\chi_{8013}(16,\cdot)\)	8013.v	445	no	\(1\)	\(1\)	\(e\left(\frac{399}{445}\right)\)	\(e\left(\frac{353}{445}\right)\)	\(e\left(\frac{288}{445}\right)\)	\(e\left(\frac{144}{445}\right)\)	\(e\left(\frac{307}{445}\right)\)	\(e\left(\frac{242}{445}\right)\)	\(e\left(\frac{139}{445}\right)\)	\(e\left(\frac{143}{445}\right)\)	\(e\left(\frac{98}{445}\right)\)	\(e\left(\frac{261}{445}\right)\)
\(\chi_{8013}(17,\cdot)\)	8013.y	534	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{178}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{191}{534}\right)\)	\(e\left(\frac{70}{267}\right)\)	\(e\left(\frac{69}{178}\right)\)	\(e\left(\frac{130}{267}\right)\)	\(e\left(\frac{153}{178}\right)\)	\(e\left(\frac{31}{89}\right)\)	\(e\left(\frac{209}{534}\right)\)	\(e\left(\frac{46}{89}\right)\)
\(\chi_{8013}(19,\cdot)\)	8013.bf	2670	no	\(-1\)	\(1\)	\(e\left(\frac{61}{445}\right)\)	\(e\left(\frac{122}{445}\right)\)	\(e\left(\frac{731}{1335}\right)\)	\(e\left(\frac{1621}{2670}\right)\)	\(e\left(\frac{183}{445}\right)\)	\(e\left(\frac{914}{1335}\right)\)	\(e\left(\frac{57}{890}\right)\)	\(e\left(\frac{859}{890}\right)\)	\(e\left(\frac{1987}{2670}\right)\)	\(e\left(\frac{244}{445}\right)\)
\(\chi_{8013}(20,\cdot)\)	8013.bd	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{543}{890}\right)\)	\(e\left(\frac{98}{445}\right)\)	\(e\left(\frac{2203}{2670}\right)\)	\(e\left(\frac{662}{1335}\right)\)	\(e\left(\frac{739}{890}\right)\)	\(e\left(\frac{581}{1335}\right)\)	\(e\left(\frac{323}{890}\right)\)	\(e\left(\frac{283}{445}\right)\)	\(e\left(\frac{283}{2670}\right)\)	\(e\left(\frac{196}{445}\right)\)
\(\chi_{8013}(22,\cdot)\)	8013.bb	890	no	\(-1\)	\(1\)	\(e\left(\frac{357}{445}\right)\)	\(e\left(\frac{269}{445}\right)\)	\(e\left(\frac{164}{445}\right)\)	\(e\left(\frac{609}{890}\right)\)	\(e\left(\frac{181}{445}\right)\)	\(e\left(\frac{76}{445}\right)\)	\(e\left(\frac{319}{890}\right)\)	\(e\left(\frac{373}{890}\right)\)	\(e\left(\frac{433}{890}\right)\)	\(e\left(\frac{93}{445}\right)\)
\(\chi_{8013}(23,\cdot)\)	8013.be	2670	yes	\(1\)	\(1\)	\(e\left(\frac{731}{890}\right)\)	\(e\left(\frac{286}{445}\right)\)	\(e\left(\frac{181}{2670}\right)\)	\(e\left(\frac{313}{2670}\right)\)	\(e\left(\frac{413}{890}\right)\)	\(e\left(\frac{1187}{1335}\right)\)	\(e\left(\frac{158}{445}\right)\)	\(e\left(\frac{117}{890}\right)\)	\(e\left(\frac{1253}{1335}\right)\)	\(e\left(\frac{127}{445}\right)\)
\(\chi_{8013}(25,\cdot)\)	8013.bc	1335	no	\(1\)	\(1\)	\(e\left(\frac{144}{445}\right)\)	\(e\left(\frac{288}{445}\right)\)	\(e\left(\frac{4}{1335}\right)\)	\(e\left(\frac{892}{1335}\right)\)	\(e\left(\frac{432}{445}\right)\)	\(e\left(\frac{436}{1335}\right)\)	\(e\left(\frac{184}{445}\right)\)	\(e\left(\frac{423}{445}\right)\)	\(e\left(\frac{1324}{1335}\right)\)	\(e\left(\frac{131}{445}\right)\)
\(\chi_{8013}(26,\cdot)\)	8013.z	890	yes	\(1\)	\(1\)	\(e\left(\frac{271}{890}\right)\)	\(e\left(\frac{271}{445}\right)\)	\(e\left(\frac{567}{890}\right)\)	\(e\left(\frac{61}{890}\right)\)	\(e\left(\frac{813}{890}\right)\)	\(e\left(\frac{419}{445}\right)\)	\(e\left(\frac{408}{445}\right)\)	\(e\left(\frac{657}{890}\right)\)	\(e\left(\frac{166}{445}\right)\)	\(e\left(\frac{97}{445}\right)\)
\(\chi_{8013}(28,\cdot)\)	8013.bf	2670	no	\(-1\)	\(1\)	\(e\left(\frac{13}{445}\right)\)	\(e\left(\frac{26}{445}\right)\)	\(e\left(\frac{878}{1335}\right)\)	\(e\left(\frac{433}{2670}\right)\)	\(e\left(\frac{39}{445}\right)\)	\(e\left(\frac{917}{1335}\right)\)	\(e\left(\frac{231}{890}\right)\)	\(e\left(\frac{577}{890}\right)\)	\(e\left(\frac{511}{2670}\right)\)	\(e\left(\frac{52}{445}\right)\)
\(\chi_{8013}(29,\cdot)\)	8013.be	2670	yes	\(1\)	\(1\)	\(e\left(\frac{409}{890}\right)\)	\(e\left(\frac{409}{445}\right)\)	\(e\left(\frac{2669}{2670}\right)\)	\(e\left(\frac{2447}{2670}\right)\)	\(e\left(\frac{337}{890}\right)\)	\(e\left(\frac{613}{1335}\right)\)	\(e\left(\frac{422}{445}\right)\)	\(e\left(\frac{673}{890}\right)\)	\(e\left(\frac{502}{1335}\right)\)	\(e\left(\frac{373}{445}\right)\)
\(\chi_{8013}(31,\cdot)\)	8013.bf	2670	no	\(-1\)	\(1\)	\(e\left(\frac{274}{445}\right)\)	\(e\left(\frac{103}{445}\right)\)	\(e\left(\frac{329}{1335}\right)\)	\(e\left(\frac{1219}{2670}\right)\)	\(e\left(\frac{377}{445}\right)\)	\(e\left(\frac{1151}{1335}\right)\)	\(e\left(\frac{453}{890}\right)\)	\(e\left(\frac{831}{890}\right)\)	\(e\left(\frac{193}{2670}\right)\)	\(e\left(\frac{206}{445}\right)\)
\(\chi_{8013}(32,\cdot)\)	8013.s	178	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{178}\right)\)	\(e\left(\frac{66}{89}\right)\)	\(e\left(\frac{55}{178}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{109}{178}\right)\)	\(e\left(\frac{16}{89}\right)\)	\(e\left(\frac{25}{178}\right)\)	\(e\left(\frac{58}{89}\right)\)	\(e\left(\frac{49}{178}\right)\)	\(e\left(\frac{43}{89}\right)\)
\(\chi_{8013}(34,\cdot)\)	8013.bc	1335	no	\(1\)	\(1\)	\(e\left(\frac{46}{445}\right)\)	\(e\left(\frac{92}{445}\right)\)	\(e\left(\frac{26}{1335}\right)\)	\(e\left(\frac{458}{1335}\right)\)	\(e\left(\frac{138}{445}\right)\)	\(e\left(\frac{164}{1335}\right)\)	\(e\left(\frac{306}{445}\right)\)	\(e\left(\frac{302}{445}\right)\)	\(e\left(\frac{596}{1335}\right)\)	\(e\left(\frac{184}{445}\right)\)
\(\chi_{8013}(35,\cdot)\)	8013.be	2670	yes	\(1\)	\(1\)	\(e\left(\frac{661}{890}\right)\)	\(e\left(\frac{216}{445}\right)\)	\(e\left(\frac{2231}{2670}\right)\)	\(e\left(\frac{893}{2670}\right)\)	\(e\left(\frac{203}{890}\right)\)	\(e\left(\frac{772}{1335}\right)\)	\(e\left(\frac{138}{445}\right)\)	\(e\left(\frac{857}{890}\right)\)	\(e\left(\frac{103}{1335}\right)\)	\(e\left(\frac{432}{445}\right)\)
\(\chi_{8013}(37,\cdot)\)	8013.m	15	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{8013}(38,\cdot)\)	8013.be	2670	yes	\(1\)	\(1\)	\(e\left(\frac{99}{890}\right)\)	\(e\left(\frac{99}{445}\right)\)	\(e\left(\frac{559}{2670}\right)\)	\(e\left(\frac{1837}{2670}\right)\)	\(e\left(\frac{297}{890}\right)\)	\(e\left(\frac{428}{1335}\right)\)	\(e\left(\frac{397}{445}\right)\)	\(e\left(\frac{263}{890}\right)\)	\(e\left(\frac{1067}{1335}\right)\)	\(e\left(\frac{198}{445}\right)\)
\(\chi_{8013}(40,\cdot)\)	8013.u	267	no	\(1\)	\(1\)	\(e\left(\frac{52}{89}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{130}{267}\right)\)	\(e\left(\frac{154}{267}\right)\)	\(e\left(\frac{67}{89}\right)\)	\(e\left(\frac{19}{267}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{43}{267}\right)\)	\(e\left(\frac{30}{89}\right)\)
\(\chi_{8013}(41,\cdot)\)	8013.be	2670	yes	\(1\)	\(1\)	\(e\left(\frac{633}{890}\right)\)	\(e\left(\frac{188}{445}\right)\)	\(e\left(\frac{203}{2670}\right)\)	\(e\left(\frac{2549}{2670}\right)\)	\(e\left(\frac{119}{890}\right)\)	\(e\left(\frac{1051}{1335}\right)\)	\(e\left(\frac{219}{445}\right)\)	\(e\left(\frac{441}{890}\right)\)	\(e\left(\frac{889}{1335}\right)\)	\(e\left(\frac{376}{445}\right)\)
\(\chi_{8013}(43,\cdot)\)	8013.v	445	no	\(1\)	\(1\)	\(e\left(\frac{32}{445}\right)\)	\(e\left(\frac{64}{445}\right)\)	\(e\left(\frac{264}{445}\right)\)	\(e\left(\frac{132}{445}\right)\)	\(e\left(\frac{96}{445}\right)\)	\(e\left(\frac{296}{445}\right)\)	\(e\left(\frac{387}{445}\right)\)	\(e\left(\frac{94}{445}\right)\)	\(e\left(\frac{164}{445}\right)\)	\(e\left(\frac{128}{445}\right)\)
\(\chi_{8013}(44,\cdot)\)	8013.z	890	yes	\(1\)	\(1\)	\(e\left(\frac{691}{890}\right)\)	\(e\left(\frac{246}{445}\right)\)	\(e\left(\frac{27}{890}\right)\)	\(e\left(\frac{681}{890}\right)\)	\(e\left(\frac{293}{890}\right)\)	\(e\left(\frac{359}{445}\right)\)	\(e\left(\frac{83}{445}\right)\)	\(e\left(\frac{667}{890}\right)\)	\(e\left(\frac{241}{445}\right)\)	\(e\left(\frac{47}{445}\right)\)
\(\chi_{8013}(46,\cdot)\)	8013.bf	2670	no	\(-1\)	\(1\)	\(e\left(\frac{354}{445}\right)\)	\(e\left(\frac{263}{445}\right)\)	\(e\left(\frac{974}{1335}\right)\)	\(e\left(\frac{529}{2670}\right)\)	\(e\left(\frac{172}{445}\right)\)	\(e\left(\frac{701}{1335}\right)\)	\(e\left(\frac{163}{890}\right)\)	\(e\left(\frac{411}{890}\right)\)	\(e\left(\frac{2653}{2670}\right)\)	\(e\left(\frac{81}{445}\right)\)
\(\chi_{8013}(47,\cdot)\)	8013.y	534	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{178}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{25}{534}\right)\)	\(e\left(\frac{251}{267}\right)\)	\(e\left(\frac{119}{178}\right)\)	\(e\left(\frac{161}{267}\right)\)	\(e\left(\frac{171}{178}\right)\)	\(e\left(\frac{87}{89}\right)\)	\(e\left(\frac{265}{534}\right)\)	\(e\left(\frac{20}{89}\right)\)

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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.