LMFDB - Group of Dirichlet characters of modulus 4027

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4027)

pari: g = idealstar(,4027,2)

Character group

sage: G.order() pari: g.no
Order	=	4026
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4026}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4027}(3,\cdot)$

First 32 of 4026 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4027}(1,\cdot)$	4027.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4027}(2,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{1247}{1342}\right)$	$e\left(\frac{125}{1342}\right)$	$e\left(\frac{576}{671}\right)$	$e\left(\frac{507}{1342}\right)$	$e\left(\frac{15}{671}\right)$	$e\left(\frac{827}{1342}\right)$	$e\left(\frac{1057}{1342}\right)$	$e\left(\frac{125}{671}\right)$	$e\left(\frac{206}{671}\right)$	$e\left(\frac{1255}{1342}\right)$
$\chi_{4027}(3,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{125}{1342}\right)$	$e\left(\frac{1}{4026}\right)$	$e\left(\frac{125}{671}\right)$	$e\left(\frac{47}{4026}\right)$	$e\left(\frac{188}{2013}\right)$	$e\left(\frac{607}{1342}\right)$	$e\left(\frac{375}{1342}\right)$	$e\left(\frac{1}{2013}\right)$	$e\left(\frac{211}{2013}\right)$	$e\left(\frac{3875}{4026}\right)$
$\chi_{4027}(4,\cdot)$	4027.m	671	yes	$1$	$1$	$e\left(\frac{576}{671}\right)$	$e\left(\frac{125}{671}\right)$	$e\left(\frac{481}{671}\right)$	$e\left(\frac{507}{671}\right)$	$e\left(\frac{30}{671}\right)$	$e\left(\frac{156}{671}\right)$	$e\left(\frac{386}{671}\right)$	$e\left(\frac{250}{671}\right)$	$e\left(\frac{412}{671}\right)$	$e\left(\frac{584}{671}\right)$
$\chi_{4027}(5,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{507}{1342}\right)$	$e\left(\frac{47}{4026}\right)$	$e\left(\frac{507}{671}\right)$	$e\left(\frac{2209}{4026}\right)$	$e\left(\frac{784}{2013}\right)$	$e\left(\frac{347}{1342}\right)$	$e\left(\frac{179}{1342}\right)$	$e\left(\frac{47}{2013}\right)$	$e\left(\frac{1865}{2013}\right)$	$e\left(\frac{955}{4026}\right)$
$\chi_{4027}(6,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{15}{671}\right)$	$e\left(\frac{188}{2013}\right)$	$e\left(\frac{30}{671}\right)$	$e\left(\frac{784}{2013}\right)$	$e\left(\frac{233}{2013}\right)$	$e\left(\frac{46}{671}\right)$	$e\left(\frac{45}{671}\right)$	$e\left(\frac{376}{2013}\right)$	$e\left(\frac{829}{2013}\right)$	$e\left(\frac{1807}{2013}\right)$
$\chi_{4027}(7,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{827}{1342}\right)$	$e\left(\frac{607}{1342}\right)$	$e\left(\frac{156}{671}\right)$	$e\left(\frac{347}{1342}\right)$	$e\left(\frac{46}{671}\right)$	$e\left(\frac{881}{1342}\right)$	$e\left(\frac{1139}{1342}\right)$	$e\left(\frac{607}{671}\right)$	$e\left(\frac{587}{671}\right)$	$e\left(\frac{941}{1342}\right)$
$\chi_{4027}(8,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{1057}{1342}\right)$	$e\left(\frac{375}{1342}\right)$	$e\left(\frac{386}{671}\right)$	$e\left(\frac{179}{1342}\right)$	$e\left(\frac{45}{671}\right)$	$e\left(\frac{1139}{1342}\right)$	$e\left(\frac{487}{1342}\right)$	$e\left(\frac{375}{671}\right)$	$e\left(\frac{618}{671}\right)$	$e\left(\frac{1081}{1342}\right)$
$\chi_{4027}(9,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{125}{671}\right)$	$e\left(\frac{1}{2013}\right)$	$e\left(\frac{250}{671}\right)$	$e\left(\frac{47}{2013}\right)$	$e\left(\frac{376}{2013}\right)$	$e\left(\frac{607}{671}\right)$	$e\left(\frac{375}{671}\right)$	$e\left(\frac{2}{2013}\right)$	$e\left(\frac{422}{2013}\right)$	$e\left(\frac{1862}{2013}\right)$
$\chi_{4027}(10,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{206}{671}\right)$	$e\left(\frac{211}{2013}\right)$	$e\left(\frac{412}{671}\right)$	$e\left(\frac{1865}{2013}\right)$	$e\left(\frac{829}{2013}\right)$	$e\left(\frac{587}{671}\right)$	$e\left(\frac{618}{671}\right)$	$e\left(\frac{422}{2013}\right)$	$e\left(\frac{470}{2013}\right)$	$e\left(\frac{347}{2013}\right)$
$\chi_{4027}(11,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{1255}{1342}\right)$	$e\left(\frac{3875}{4026}\right)$	$e\left(\frac{584}{671}\right)$	$e\left(\frac{955}{4026}\right)$	$e\left(\frac{1807}{2013}\right)$	$e\left(\frac{941}{1342}\right)$	$e\left(\frac{1081}{1342}\right)$	$e\left(\frac{1862}{2013}\right)$	$e\left(\frac{347}{2013}\right)$	$e\left(\frac{2671}{4026}\right)$
$\chi_{4027}(12,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{1277}{1342}\right)$	$e\left(\frac{751}{4026}\right)$	$e\left(\frac{606}{671}\right)$	$e\left(\frac{3089}{4026}\right)$	$e\left(\frac{278}{2013}\right)$	$e\left(\frac{919}{1342}\right)$	$e\left(\frac{1147}{1342}\right)$	$e\left(\frac{751}{2013}\right)$	$e\left(\frac{1447}{2013}\right)$	$e\left(\frac{3353}{4026}\right)$
$\chi_{4027}(13,\cdot)$	4027.h	61	yes	$1$	$1$	$e\left(\frac{9}{61}\right)$	$e\left(\frac{1}{61}\right)$	$e\left(\frac{18}{61}\right)$	$e\left(\frac{47}{61}\right)$	$e\left(\frac{10}{61}\right)$	$e\left(\frac{52}{61}\right)$	$e\left(\frac{27}{61}\right)$	$e\left(\frac{2}{61}\right)$	$e\left(\frac{56}{61}\right)$	$e\left(\frac{32}{61}\right)$
$\chi_{4027}(14,\cdot)$	4027.e	11	yes	$1$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{4027}(15,\cdot)$	4027.m	671	yes	$1$	$1$	$e\left(\frac{316}{671}\right)$	$e\left(\frac{8}{671}\right)$	$e\left(\frac{632}{671}\right)$	$e\left(\frac{376}{671}\right)$	$e\left(\frac{324}{671}\right)$	$e\left(\frac{477}{671}\right)$	$e\left(\frac{277}{671}\right)$	$e\left(\frac{16}{671}\right)$	$e\left(\frac{21}{671}\right)$	$e\left(\frac{134}{671}\right)$
$\chi_{4027}(16,\cdot)$	4027.m	671	yes	$1$	$1$	$e\left(\frac{481}{671}\right)$	$e\left(\frac{250}{671}\right)$	$e\left(\frac{291}{671}\right)$	$e\left(\frac{343}{671}\right)$	$e\left(\frac{60}{671}\right)$	$e\left(\frac{312}{671}\right)$	$e\left(\frac{101}{671}\right)$	$e\left(\frac{500}{671}\right)$	$e\left(\frac{153}{671}\right)$	$e\left(\frac{497}{671}\right)$
$\chi_{4027}(17,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{315}{671}\right)$	$e\left(\frac{593}{2013}\right)$	$e\left(\frac{630}{671}\right)$	$e\left(\frac{1702}{2013}\right)$	$e\left(\frac{1538}{2013}\right)$	$e\left(\frac{295}{671}\right)$	$e\left(\frac{274}{671}\right)$	$e\left(\frac{1186}{2013}\right)$	$e\left(\frac{634}{2013}\right)$	$e\left(\frac{1042}{2013}\right)$
$\chi_{4027}(18,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{155}{1342}\right)$	$e\left(\frac{377}{4026}\right)$	$e\left(\frac{155}{671}\right)$	$e\left(\frac{1615}{4026}\right)$	$e\left(\frac{421}{2013}\right)$	$e\left(\frac{699}{1342}\right)$	$e\left(\frac{465}{1342}\right)$	$e\left(\frac{377}{2013}\right)$	$e\left(\frac{1040}{2013}\right)$	$e\left(\frac{3463}{4026}\right)$
$\chi_{4027}(19,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{325}{671}\right)$	$e\left(\frac{271}{2013}\right)$	$e\left(\frac{650}{671}\right)$	$e\left(\frac{659}{2013}\right)$	$e\left(\frac{1246}{2013}\right)$	$e\left(\frac{102}{671}\right)$	$e\left(\frac{304}{671}\right)$	$e\left(\frac{542}{2013}\right)$	$e\left(\frac{1634}{2013}\right)$	$e\left(\frac{1352}{2013}\right)$
$\chi_{4027}(20,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{317}{1342}\right)$	$e\left(\frac{797}{4026}\right)$	$e\left(\frac{317}{671}\right)$	$e\left(\frac{1225}{4026}\right)$	$e\left(\frac{874}{2013}\right)$	$e\left(\frac{659}{1342}\right)$	$e\left(\frac{951}{1342}\right)$	$e\left(\frac{797}{2013}\right)$	$e\left(\frac{1088}{2013}\right)$	$e\left(\frac{433}{4026}\right)$
$\chi_{4027}(21,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{476}{671}\right)$	$e\left(\frac{911}{2013}\right)$	$e\left(\frac{281}{671}\right)$	$e\left(\frac{544}{2013}\right)$	$e\left(\frac{326}{2013}\right)$	$e\left(\frac{73}{671}\right)$	$e\left(\frac{86}{671}\right)$	$e\left(\frac{1822}{2013}\right)$	$e\left(\frac{1972}{2013}\right)$	$e\left(\frac{1336}{2013}\right)$
$\chi_{4027}(22,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{580}{671}\right)$	$e\left(\frac{112}{2013}\right)$	$e\left(\frac{489}{671}\right)$	$e\left(\frac{1238}{2013}\right)$	$e\left(\frac{1852}{2013}\right)$	$e\left(\frac{213}{671}\right)$	$e\left(\frac{398}{671}\right)$	$e\left(\frac{224}{2013}\right)$	$e\left(\frac{965}{2013}\right)$	$e\left(\frac{1205}{2013}\right)$
$\chi_{4027}(23,\cdot)$	4027.l	366	yes	$-1$	$1$	$e\left(\frac{7}{122}\right)$	$e\left(\frac{43}{366}\right)$	$e\left(\frac{7}{61}\right)$	$e\left(\frac{191}{366}\right)$	$e\left(\frac{32}{183}\right)$	$e\left(\frac{115}{122}\right)$	$e\left(\frac{21}{122}\right)$	$e\left(\frac{43}{183}\right)$	$e\left(\frac{106}{183}\right)$	$e\left(\frac{95}{366}\right)$
$\chi_{4027}(24,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{591}{671}\right)$	$e\left(\frac{563}{2013}\right)$	$e\left(\frac{511}{671}\right)$	$e\left(\frac{292}{2013}\right)$	$e\left(\frac{323}{2013}\right)$	$e\left(\frac{202}{671}\right)$	$e\left(\frac{431}{671}\right)$	$e\left(\frac{1126}{2013}\right)$	$e\left(\frac{52}{2013}\right)$	$e\left(\frac{1546}{2013}\right)$
$\chi_{4027}(25,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{507}{671}\right)$	$e\left(\frac{47}{2013}\right)$	$e\left(\frac{343}{671}\right)$	$e\left(\frac{196}{2013}\right)$	$e\left(\frac{1568}{2013}\right)$	$e\left(\frac{347}{671}\right)$	$e\left(\frac{179}{671}\right)$	$e\left(\frac{94}{2013}\right)$	$e\left(\frac{1717}{2013}\right)$	$e\left(\frac{955}{2013}\right)$
$\chi_{4027}(26,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{103}{1342}\right)$	$e\left(\frac{147}{1342}\right)$	$e\left(\frac{103}{671}\right)$	$e\left(\frac{199}{1342}\right)$	$e\left(\frac{125}{671}\right)$	$e\left(\frac{629}{1342}\right)$	$e\left(\frac{309}{1342}\right)$	$e\left(\frac{147}{671}\right)$	$e\left(\frac{151}{671}\right)$	$e\left(\frac{617}{1342}\right)$
$\chi_{4027}(27,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{375}{1342}\right)$	$e\left(\frac{1}{1342}\right)$	$e\left(\frac{375}{671}\right)$	$e\left(\frac{47}{1342}\right)$	$e\left(\frac{188}{671}\right)$	$e\left(\frac{479}{1342}\right)$	$e\left(\frac{1125}{1342}\right)$	$e\left(\frac{1}{671}\right)$	$e\left(\frac{211}{671}\right)$	$e\left(\frac{1191}{1342}\right)$
$\chi_{4027}(28,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{637}{1342}\right)$	$e\left(\frac{857}{1342}\right)$	$e\left(\frac{637}{671}\right)$	$e\left(\frac{19}{1342}\right)$	$e\left(\frac{76}{671}\right)$	$e\left(\frac{1193}{1342}\right)$	$e\left(\frac{569}{1342}\right)$	$e\left(\frac{186}{671}\right)$	$e\left(\frac{328}{671}\right)$	$e\left(\frac{767}{1342}\right)$
$\chi_{4027}(29,\cdot)$	4027.o	2013	yes	$1$	$1$	$e\left(\frac{118}{671}\right)$	$e\left(\frac{629}{2013}\right)$	$e\left(\frac{236}{671}\right)$	$e\left(\frac{1381}{2013}\right)$	$e\left(\frac{983}{2013}\right)$	$e\left(\frac{4}{671}\right)$	$e\left(\frac{354}{671}\right)$	$e\left(\frac{1258}{2013}\right)$	$e\left(\frac{1735}{2013}\right)$	$e\left(\frac{1645}{2013}\right)$
$\chi_{4027}(30,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{537}{1342}\right)$	$e\left(\frac{141}{1342}\right)$	$e\left(\frac{537}{671}\right)$	$e\left(\frac{1259}{1342}\right)$	$e\left(\frac{339}{671}\right)$	$e\left(\frac{439}{1342}\right)$	$e\left(\frac{269}{1342}\right)$	$e\left(\frac{141}{671}\right)$	$e\left(\frac{227}{671}\right)$	$e\left(\frac{181}{1342}\right)$
$\chi_{4027}(31,\cdot)$	4027.p	4026	yes	$-1$	$1$	$e\left(\frac{857}{1342}\right)$	$e\left(\frac{3539}{4026}\right)$	$e\left(\frac{186}{671}\right)$	$e\left(\frac{1267}{4026}\right)$	$e\left(\frac{1042}{2013}\right)$	$e\left(\frac{973}{1342}\right)$	$e\left(\frac{1229}{1342}\right)$	$e\left(\frac{1526}{2013}\right)$	$e\left(\frac{1919}{2013}\right)$	$e\left(\frac{1069}{4026}\right)$
$\chi_{4027}(32,\cdot)$	4027.n	1342	yes	$-1$	$1$	$e\left(\frac{867}{1342}\right)$	$e\left(\frac{625}{1342}\right)$	$e\left(\frac{196}{671}\right)$	$e\left(\frac{1193}{1342}\right)$	$e\left(\frac{75}{671}\right)$	$e\left(\frac{109}{1342}\right)$	$e\left(\frac{1259}{1342}\right)$	$e\left(\frac{625}{671}\right)$	$e\left(\frac{359}{671}\right)$	$e\left(\frac{907}{1342}\right)$

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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	$4027$
Structure	\(C_{4026}\)
Order	$4026$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4027}(1,\cdot)\)	4027.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4027}(2,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{1247}{1342}\right)\)	\(e\left(\frac{125}{1342}\right)\)	\(e\left(\frac{576}{671}\right)\)	\(e\left(\frac{507}{1342}\right)\)	\(e\left(\frac{15}{671}\right)\)	\(e\left(\frac{827}{1342}\right)\)	\(e\left(\frac{1057}{1342}\right)\)	\(e\left(\frac{125}{671}\right)\)	\(e\left(\frac{206}{671}\right)\)	\(e\left(\frac{1255}{1342}\right)\)
\(\chi_{4027}(3,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{1342}\right)\)	\(e\left(\frac{1}{4026}\right)\)	\(e\left(\frac{125}{671}\right)\)	\(e\left(\frac{47}{4026}\right)\)	\(e\left(\frac{188}{2013}\right)\)	\(e\left(\frac{607}{1342}\right)\)	\(e\left(\frac{375}{1342}\right)\)	\(e\left(\frac{1}{2013}\right)\)	\(e\left(\frac{211}{2013}\right)\)	\(e\left(\frac{3875}{4026}\right)\)
\(\chi_{4027}(4,\cdot)\)	4027.m	671	yes	\(1\)	\(1\)	\(e\left(\frac{576}{671}\right)\)	\(e\left(\frac{125}{671}\right)\)	\(e\left(\frac{481}{671}\right)\)	\(e\left(\frac{507}{671}\right)\)	\(e\left(\frac{30}{671}\right)\)	\(e\left(\frac{156}{671}\right)\)	\(e\left(\frac{386}{671}\right)\)	\(e\left(\frac{250}{671}\right)\)	\(e\left(\frac{412}{671}\right)\)	\(e\left(\frac{584}{671}\right)\)
\(\chi_{4027}(5,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{507}{1342}\right)\)	\(e\left(\frac{47}{4026}\right)\)	\(e\left(\frac{507}{671}\right)\)	\(e\left(\frac{2209}{4026}\right)\)	\(e\left(\frac{784}{2013}\right)\)	\(e\left(\frac{347}{1342}\right)\)	\(e\left(\frac{179}{1342}\right)\)	\(e\left(\frac{47}{2013}\right)\)	\(e\left(\frac{1865}{2013}\right)\)	\(e\left(\frac{955}{4026}\right)\)
\(\chi_{4027}(6,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{15}{671}\right)\)	\(e\left(\frac{188}{2013}\right)\)	\(e\left(\frac{30}{671}\right)\)	\(e\left(\frac{784}{2013}\right)\)	\(e\left(\frac{233}{2013}\right)\)	\(e\left(\frac{46}{671}\right)\)	\(e\left(\frac{45}{671}\right)\)	\(e\left(\frac{376}{2013}\right)\)	\(e\left(\frac{829}{2013}\right)\)	\(e\left(\frac{1807}{2013}\right)\)
\(\chi_{4027}(7,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{827}{1342}\right)\)	\(e\left(\frac{607}{1342}\right)\)	\(e\left(\frac{156}{671}\right)\)	\(e\left(\frac{347}{1342}\right)\)	\(e\left(\frac{46}{671}\right)\)	\(e\left(\frac{881}{1342}\right)\)	\(e\left(\frac{1139}{1342}\right)\)	\(e\left(\frac{607}{671}\right)\)	\(e\left(\frac{587}{671}\right)\)	\(e\left(\frac{941}{1342}\right)\)
\(\chi_{4027}(8,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{1057}{1342}\right)\)	\(e\left(\frac{375}{1342}\right)\)	\(e\left(\frac{386}{671}\right)\)	\(e\left(\frac{179}{1342}\right)\)	\(e\left(\frac{45}{671}\right)\)	\(e\left(\frac{1139}{1342}\right)\)	\(e\left(\frac{487}{1342}\right)\)	\(e\left(\frac{375}{671}\right)\)	\(e\left(\frac{618}{671}\right)\)	\(e\left(\frac{1081}{1342}\right)\)
\(\chi_{4027}(9,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{125}{671}\right)\)	\(e\left(\frac{1}{2013}\right)\)	\(e\left(\frac{250}{671}\right)\)	\(e\left(\frac{47}{2013}\right)\)	\(e\left(\frac{376}{2013}\right)\)	\(e\left(\frac{607}{671}\right)\)	\(e\left(\frac{375}{671}\right)\)	\(e\left(\frac{2}{2013}\right)\)	\(e\left(\frac{422}{2013}\right)\)	\(e\left(\frac{1862}{2013}\right)\)
\(\chi_{4027}(10,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{206}{671}\right)\)	\(e\left(\frac{211}{2013}\right)\)	\(e\left(\frac{412}{671}\right)\)	\(e\left(\frac{1865}{2013}\right)\)	\(e\left(\frac{829}{2013}\right)\)	\(e\left(\frac{587}{671}\right)\)	\(e\left(\frac{618}{671}\right)\)	\(e\left(\frac{422}{2013}\right)\)	\(e\left(\frac{470}{2013}\right)\)	\(e\left(\frac{347}{2013}\right)\)
\(\chi_{4027}(11,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{1255}{1342}\right)\)	\(e\left(\frac{3875}{4026}\right)\)	\(e\left(\frac{584}{671}\right)\)	\(e\left(\frac{955}{4026}\right)\)	\(e\left(\frac{1807}{2013}\right)\)	\(e\left(\frac{941}{1342}\right)\)	\(e\left(\frac{1081}{1342}\right)\)	\(e\left(\frac{1862}{2013}\right)\)	\(e\left(\frac{347}{2013}\right)\)	\(e\left(\frac{2671}{4026}\right)\)
\(\chi_{4027}(12,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{1277}{1342}\right)\)	\(e\left(\frac{751}{4026}\right)\)	\(e\left(\frac{606}{671}\right)\)	\(e\left(\frac{3089}{4026}\right)\)	\(e\left(\frac{278}{2013}\right)\)	\(e\left(\frac{919}{1342}\right)\)	\(e\left(\frac{1147}{1342}\right)\)	\(e\left(\frac{751}{2013}\right)\)	\(e\left(\frac{1447}{2013}\right)\)	\(e\left(\frac{3353}{4026}\right)\)
\(\chi_{4027}(13,\cdot)\)	4027.h	61	yes	\(1\)	\(1\)	\(e\left(\frac{9}{61}\right)\)	\(e\left(\frac{1}{61}\right)\)	\(e\left(\frac{18}{61}\right)\)	\(e\left(\frac{47}{61}\right)\)	\(e\left(\frac{10}{61}\right)\)	\(e\left(\frac{52}{61}\right)\)	\(e\left(\frac{27}{61}\right)\)	\(e\left(\frac{2}{61}\right)\)	\(e\left(\frac{56}{61}\right)\)	\(e\left(\frac{32}{61}\right)\)
\(\chi_{4027}(14,\cdot)\)	4027.e	11	yes	\(1\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{4027}(15,\cdot)\)	4027.m	671	yes	\(1\)	\(1\)	\(e\left(\frac{316}{671}\right)\)	\(e\left(\frac{8}{671}\right)\)	\(e\left(\frac{632}{671}\right)\)	\(e\left(\frac{376}{671}\right)\)	\(e\left(\frac{324}{671}\right)\)	\(e\left(\frac{477}{671}\right)\)	\(e\left(\frac{277}{671}\right)\)	\(e\left(\frac{16}{671}\right)\)	\(e\left(\frac{21}{671}\right)\)	\(e\left(\frac{134}{671}\right)\)
\(\chi_{4027}(16,\cdot)\)	4027.m	671	yes	\(1\)	\(1\)	\(e\left(\frac{481}{671}\right)\)	\(e\left(\frac{250}{671}\right)\)	\(e\left(\frac{291}{671}\right)\)	\(e\left(\frac{343}{671}\right)\)	\(e\left(\frac{60}{671}\right)\)	\(e\left(\frac{312}{671}\right)\)	\(e\left(\frac{101}{671}\right)\)	\(e\left(\frac{500}{671}\right)\)	\(e\left(\frac{153}{671}\right)\)	\(e\left(\frac{497}{671}\right)\)
\(\chi_{4027}(17,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{315}{671}\right)\)	\(e\left(\frac{593}{2013}\right)\)	\(e\left(\frac{630}{671}\right)\)	\(e\left(\frac{1702}{2013}\right)\)	\(e\left(\frac{1538}{2013}\right)\)	\(e\left(\frac{295}{671}\right)\)	\(e\left(\frac{274}{671}\right)\)	\(e\left(\frac{1186}{2013}\right)\)	\(e\left(\frac{634}{2013}\right)\)	\(e\left(\frac{1042}{2013}\right)\)
\(\chi_{4027}(18,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{155}{1342}\right)\)	\(e\left(\frac{377}{4026}\right)\)	\(e\left(\frac{155}{671}\right)\)	\(e\left(\frac{1615}{4026}\right)\)	\(e\left(\frac{421}{2013}\right)\)	\(e\left(\frac{699}{1342}\right)\)	\(e\left(\frac{465}{1342}\right)\)	\(e\left(\frac{377}{2013}\right)\)	\(e\left(\frac{1040}{2013}\right)\)	\(e\left(\frac{3463}{4026}\right)\)
\(\chi_{4027}(19,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{325}{671}\right)\)	\(e\left(\frac{271}{2013}\right)\)	\(e\left(\frac{650}{671}\right)\)	\(e\left(\frac{659}{2013}\right)\)	\(e\left(\frac{1246}{2013}\right)\)	\(e\left(\frac{102}{671}\right)\)	\(e\left(\frac{304}{671}\right)\)	\(e\left(\frac{542}{2013}\right)\)	\(e\left(\frac{1634}{2013}\right)\)	\(e\left(\frac{1352}{2013}\right)\)
\(\chi_{4027}(20,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{317}{1342}\right)\)	\(e\left(\frac{797}{4026}\right)\)	\(e\left(\frac{317}{671}\right)\)	\(e\left(\frac{1225}{4026}\right)\)	\(e\left(\frac{874}{2013}\right)\)	\(e\left(\frac{659}{1342}\right)\)	\(e\left(\frac{951}{1342}\right)\)	\(e\left(\frac{797}{2013}\right)\)	\(e\left(\frac{1088}{2013}\right)\)	\(e\left(\frac{433}{4026}\right)\)
\(\chi_{4027}(21,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{476}{671}\right)\)	\(e\left(\frac{911}{2013}\right)\)	\(e\left(\frac{281}{671}\right)\)	\(e\left(\frac{544}{2013}\right)\)	\(e\left(\frac{326}{2013}\right)\)	\(e\left(\frac{73}{671}\right)\)	\(e\left(\frac{86}{671}\right)\)	\(e\left(\frac{1822}{2013}\right)\)	\(e\left(\frac{1972}{2013}\right)\)	\(e\left(\frac{1336}{2013}\right)\)
\(\chi_{4027}(22,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{580}{671}\right)\)	\(e\left(\frac{112}{2013}\right)\)	\(e\left(\frac{489}{671}\right)\)	\(e\left(\frac{1238}{2013}\right)\)	\(e\left(\frac{1852}{2013}\right)\)	\(e\left(\frac{213}{671}\right)\)	\(e\left(\frac{398}{671}\right)\)	\(e\left(\frac{224}{2013}\right)\)	\(e\left(\frac{965}{2013}\right)\)	\(e\left(\frac{1205}{2013}\right)\)
\(\chi_{4027}(23,\cdot)\)	4027.l	366	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{122}\right)\)	\(e\left(\frac{43}{366}\right)\)	\(e\left(\frac{7}{61}\right)\)	\(e\left(\frac{191}{366}\right)\)	\(e\left(\frac{32}{183}\right)\)	\(e\left(\frac{115}{122}\right)\)	\(e\left(\frac{21}{122}\right)\)	\(e\left(\frac{43}{183}\right)\)	\(e\left(\frac{106}{183}\right)\)	\(e\left(\frac{95}{366}\right)\)
\(\chi_{4027}(24,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{591}{671}\right)\)	\(e\left(\frac{563}{2013}\right)\)	\(e\left(\frac{511}{671}\right)\)	\(e\left(\frac{292}{2013}\right)\)	\(e\left(\frac{323}{2013}\right)\)	\(e\left(\frac{202}{671}\right)\)	\(e\left(\frac{431}{671}\right)\)	\(e\left(\frac{1126}{2013}\right)\)	\(e\left(\frac{52}{2013}\right)\)	\(e\left(\frac{1546}{2013}\right)\)
\(\chi_{4027}(25,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{507}{671}\right)\)	\(e\left(\frac{47}{2013}\right)\)	\(e\left(\frac{343}{671}\right)\)	\(e\left(\frac{196}{2013}\right)\)	\(e\left(\frac{1568}{2013}\right)\)	\(e\left(\frac{347}{671}\right)\)	\(e\left(\frac{179}{671}\right)\)	\(e\left(\frac{94}{2013}\right)\)	\(e\left(\frac{1717}{2013}\right)\)	\(e\left(\frac{955}{2013}\right)\)
\(\chi_{4027}(26,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{103}{1342}\right)\)	\(e\left(\frac{147}{1342}\right)\)	\(e\left(\frac{103}{671}\right)\)	\(e\left(\frac{199}{1342}\right)\)	\(e\left(\frac{125}{671}\right)\)	\(e\left(\frac{629}{1342}\right)\)	\(e\left(\frac{309}{1342}\right)\)	\(e\left(\frac{147}{671}\right)\)	\(e\left(\frac{151}{671}\right)\)	\(e\left(\frac{617}{1342}\right)\)
\(\chi_{4027}(27,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{375}{1342}\right)\)	\(e\left(\frac{1}{1342}\right)\)	\(e\left(\frac{375}{671}\right)\)	\(e\left(\frac{47}{1342}\right)\)	\(e\left(\frac{188}{671}\right)\)	\(e\left(\frac{479}{1342}\right)\)	\(e\left(\frac{1125}{1342}\right)\)	\(e\left(\frac{1}{671}\right)\)	\(e\left(\frac{211}{671}\right)\)	\(e\left(\frac{1191}{1342}\right)\)
\(\chi_{4027}(28,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{637}{1342}\right)\)	\(e\left(\frac{857}{1342}\right)\)	\(e\left(\frac{637}{671}\right)\)	\(e\left(\frac{19}{1342}\right)\)	\(e\left(\frac{76}{671}\right)\)	\(e\left(\frac{1193}{1342}\right)\)	\(e\left(\frac{569}{1342}\right)\)	\(e\left(\frac{186}{671}\right)\)	\(e\left(\frac{328}{671}\right)\)	\(e\left(\frac{767}{1342}\right)\)
\(\chi_{4027}(29,\cdot)\)	4027.o	2013	yes	\(1\)	\(1\)	\(e\left(\frac{118}{671}\right)\)	\(e\left(\frac{629}{2013}\right)\)	\(e\left(\frac{236}{671}\right)\)	\(e\left(\frac{1381}{2013}\right)\)	\(e\left(\frac{983}{2013}\right)\)	\(e\left(\frac{4}{671}\right)\)	\(e\left(\frac{354}{671}\right)\)	\(e\left(\frac{1258}{2013}\right)\)	\(e\left(\frac{1735}{2013}\right)\)	\(e\left(\frac{1645}{2013}\right)\)
\(\chi_{4027}(30,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{537}{1342}\right)\)	\(e\left(\frac{141}{1342}\right)\)	\(e\left(\frac{537}{671}\right)\)	\(e\left(\frac{1259}{1342}\right)\)	\(e\left(\frac{339}{671}\right)\)	\(e\left(\frac{439}{1342}\right)\)	\(e\left(\frac{269}{1342}\right)\)	\(e\left(\frac{141}{671}\right)\)	\(e\left(\frac{227}{671}\right)\)	\(e\left(\frac{181}{1342}\right)\)
\(\chi_{4027}(31,\cdot)\)	4027.p	4026	yes	\(-1\)	\(1\)	\(e\left(\frac{857}{1342}\right)\)	\(e\left(\frac{3539}{4026}\right)\)	\(e\left(\frac{186}{671}\right)\)	\(e\left(\frac{1267}{4026}\right)\)	\(e\left(\frac{1042}{2013}\right)\)	\(e\left(\frac{973}{1342}\right)\)	\(e\left(\frac{1229}{1342}\right)\)	\(e\left(\frac{1526}{2013}\right)\)	\(e\left(\frac{1919}{2013}\right)\)	\(e\left(\frac{1069}{4026}\right)\)
\(\chi_{4027}(32,\cdot)\)	4027.n	1342	yes	\(-1\)	\(1\)	\(e\left(\frac{867}{1342}\right)\)	\(e\left(\frac{625}{1342}\right)\)	\(e\left(\frac{196}{671}\right)\)	\(e\left(\frac{1193}{1342}\right)\)	\(e\left(\frac{75}{671}\right)\)	\(e\left(\frac{109}{1342}\right)\)	\(e\left(\frac{1259}{1342}\right)\)	\(e\left(\frac{625}{671}\right)\)	\(e\left(\frac{359}{671}\right)\)	\(e\left(\frac{907}{1342}\right)\)

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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.