LMFDB - Group of Dirichlet characters of modulus 4011

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4011)

pari: g = idealstar(,4011,2)

Character group

sage: G.order() pari: g.no
Order	=	2280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{570}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4011}(2675,\cdot)$, $\chi_{4011}(2866,\cdot)$, $\chi_{4011}(2311,\cdot)$

First 32 of 2280 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{4011}(1,\cdot)$	4011.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4011}(2,\cdot)$	4011.ci	570	yes	$-1$	$1$	$e\left(\frac{203}{570}\right)$	$e\left(\frac{203}{285}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{13}{190}\right)$	$e\left(\frac{29}{285}\right)$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{89}{95}\right)$	$e\left(\frac{121}{285}\right)$	$e\left(\frac{301}{570}\right)$	$e\left(\frac{256}{285}\right)$
$\chi_{4011}(4,\cdot)$	4011.ce	285	no	$1$	$1$	$e\left(\frac{203}{285}\right)$	$e\left(\frac{121}{285}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{58}{285}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{242}{285}\right)$	$e\left(\frac{16}{285}\right)$	$e\left(\frac{227}{285}\right)$
$\chi_{4011}(5,\cdot)$	4011.bs	114	yes	$1$	$1$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{49}{114}\right)$
$\chi_{4011}(8,\cdot)$	4011.ca	190	no	$-1$	$1$	$e\left(\frac{13}{190}\right)$	$e\left(\frac{13}{95}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{39}{190}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{26}{95}\right)$	$e\left(\frac{111}{190}\right)$	$e\left(\frac{66}{95}\right)$
$\chi_{4011}(10,\cdot)$	4011.cg	570	no	$-1$	$1$	$e\left(\frac{29}{285}\right)$	$e\left(\frac{58}{285}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{383}{570}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{173}{190}\right)$	$e\left(\frac{116}{285}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{187}{570}\right)$
$\chi_{4011}(11,\cdot)$	4011.br	114	yes	$1$	$1$	$e\left(\frac{59}{114}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{89}{114}\right)$
$\chi_{4011}(13,\cdot)$	4011.cc	190	no	$-1$	$1$	$e\left(\frac{89}{95}\right)$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{37}{38}\right)$	$e\left(\frac{77}{95}\right)$	$e\left(\frac{173}{190}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{99}{190}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{51}{190}\right)$	$e\left(\frac{17}{190}\right)$
$\chi_{4011}(16,\cdot)$	4011.ce	285	no	$1$	$1$	$e\left(\frac{121}{285}\right)$	$e\left(\frac{242}{285}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{26}{95}\right)$	$e\left(\frac{116}{285}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{199}{285}\right)$	$e\left(\frac{32}{285}\right)$	$e\left(\frac{169}{285}\right)$
$\chi_{4011}(17,\cdot)$	4011.ck	570	yes	$1$	$1$	$e\left(\frac{301}{570}\right)$	$e\left(\frac{16}{285}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{111}{190}\right)$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{1}{114}\right)$	$e\left(\frac{51}{190}\right)$	$e\left(\frac{32}{285}\right)$	$e\left(\frac{61}{285}\right)$	$e\left(\frac{199}{570}\right)$
$\chi_{4011}(19,\cdot)$	4011.cf	570	no	$1$	$1$	$e\left(\frac{256}{285}\right)$	$e\left(\frac{227}{285}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{187}{570}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{17}{190}\right)$	$e\left(\frac{169}{285}\right)$	$e\left(\frac{199}{570}\right)$	$e\left(\frac{49}{285}\right)$
$\chi_{4011}(20,\cdot)$	4011.by	190	yes	$1$	$1$	$e\left(\frac{87}{190}\right)$	$e\left(\frac{87}{95}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{71}{190}\right)$	$e\left(\frac{147}{190}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{161}{190}\right)$	$e\left(\frac{79}{95}\right)$	$e\left(\frac{17}{95}\right)$	$e\left(\frac{43}{190}\right)$
$\chi_{4011}(22,\cdot)$	4011.cb	190	no	$-1$	$1$	$e\left(\frac{83}{95}\right)$	$e\left(\frac{71}{95}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{59}{95}\right)$	$e\left(\frac{78}{95}\right)$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{4}{95}\right)$	$e\left(\frac{47}{95}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{129}{190}\right)$
$\chi_{4011}(23,\cdot)$	4011.ci	570	yes	$-1$	$1$	$e\left(\frac{113}{570}\right)$	$e\left(\frac{113}{285}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{113}{190}\right)$	$e\left(\frac{179}{285}\right)$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{94}{95}\right)$	$e\left(\frac{226}{285}\right)$	$e\left(\frac{541}{570}\right)$	$e\left(\frac{106}{285}\right)$
$\chi_{4011}(25,\cdot)$	4011.bo	57	no	$1$	$1$	$e\left(\frac{28}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{9}{19}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{23}{57}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{49}{57}\right)$
$\chi_{4011}(26,\cdot)$	4011.ck	570	yes	$1$	$1$	$e\left(\frac{167}{570}\right)$	$e\left(\frac{167}{285}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{167}{190}\right)$	$e\left(\frac{7}{570}\right)$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{87}{190}\right)$	$e\left(\frac{49}{285}\right)$	$e\left(\frac{227}{285}\right)$	$e\left(\frac{563}{570}\right)$
$\chi_{4011}(29,\cdot)$	4011.bz	190	no	$1$	$1$	$e\left(\frac{27}{190}\right)$	$e\left(\frac{27}{95}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{81}{190}\right)$	$e\left(\frac{31}{95}\right)$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{43}{95}\right)$	$e\left(\frac{54}{95}\right)$	$e\left(\frac{99}{190}\right)$	$e\left(\frac{33}{190}\right)$
$\chi_{4011}(31,\cdot)$	4011.bu	114	no	$1$	$1$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{41}{57}\right)$	$e\left(\frac{101}{114}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{85}{114}\right)$	$e\left(\frac{109}{114}\right)$	$e\left(\frac{25}{38}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{43}{57}\right)$
$\chi_{4011}(32,\cdot)$	4011.bq	114	yes	$-1$	$1$	$e\left(\frac{89}{114}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{83}{114}\right)$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{67}{114}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{73}{114}\right)$	$e\left(\frac{28}{57}\right)$
$\chi_{4011}(34,\cdot)$	4011.cc	190	no	$-1$	$1$	$e\left(\frac{84}{95}\right)$	$e\left(\frac{73}{95}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{62}{95}\right)$	$e\left(\frac{143}{190}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{39}{190}\right)$	$e\left(\frac{51}{95}\right)$	$e\left(\frac{141}{190}\right)$	$e\left(\frac{47}{190}\right)$
$\chi_{4011}(37,\cdot)$	4011.bw	114	no	$-1$	$1$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{16}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{5}{114}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{85}{114}\right)$
$\chi_{4011}(38,\cdot)$	4011.bt	114	yes	$-1$	$1$	$e\left(\frac{29}{114}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{49}{114}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{4}{57}\right)$
$\chi_{4011}(40,\cdot)$	4011.cg	570	no	$-1$	$1$	$e\left(\frac{232}{285}\right)$	$e\left(\frac{179}{285}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{42}{95}\right)$	$e\left(\frac{499}{570}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{149}{190}\right)$	$e\left(\frac{73}{285}\right)$	$e\left(\frac{403}{570}\right)$	$e\left(\frac{71}{570}\right)$
$\chi_{4011}(41,\cdot)$	4011.bk	38	yes	$-1$	$1$	$e\left(\frac{27}{38}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{29}{38}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{4011}(43,\cdot)$	4011.bp	95	no	$1$	$1$	$e\left(\frac{81}{95}\right)$	$e\left(\frac{67}{95}\right)$	$e\left(\frac{2}{19}\right)$	$e\left(\frac{53}{95}\right)$	$e\left(\frac{91}{95}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{68}{95}\right)$	$e\left(\frac{39}{95}\right)$	$e\left(\frac{12}{95}\right)$	$e\left(\frac{4}{95}\right)$
$\chi_{4011}(44,\cdot)$	4011.cj	570	yes	$1$	$1$	$e\left(\frac{131}{570}\right)$	$e\left(\frac{131}{285}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{131}{190}\right)$	$e\left(\frac{263}{285}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{93}{95}\right)$	$e\left(\frac{262}{285}\right)$	$e\left(\frac{37}{570}\right)$	$e\left(\frac{329}{570}\right)$
$\chi_{4011}(46,\cdot)$	4011.ce	285	no	$1$	$1$	$e\left(\frac{158}{285}\right)$	$e\left(\frac{31}{285}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{63}{95}\right)$	$e\left(\frac{208}{285}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{88}{95}\right)$	$e\left(\frac{62}{285}\right)$	$e\left(\frac{136}{285}\right)$	$e\left(\frac{77}{285}\right)$
$\chi_{4011}(47,\cdot)$	4011.cl	570	yes	$-1$	$1$	$e\left(\frac{371}{570}\right)$	$e\left(\frac{86}{285}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{181}{190}\right)$	$e\left(\frac{391}{570}\right)$	$e\left(\frac{49}{57}\right)$	$e\left(\frac{1}{190}\right)$	$e\left(\frac{172}{285}\right)$	$e\left(\frac{221}{285}\right)$	$e\left(\frac{232}{285}\right)$
$\chi_{4011}(50,\cdot)$	4011.ca	190	no	$-1$	$1$	$e\left(\frac{161}{190}\right)$	$e\left(\frac{66}{95}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{103}{190}\right)$	$e\left(\frac{23}{95}\right)$	$e\left(\frac{35}{38}\right)$	$e\left(\frac{84}{95}\right)$	$e\left(\frac{37}{95}\right)$	$e\left(\frac{147}{190}\right)$	$e\left(\frac{72}{95}\right)$
$\chi_{4011}(52,\cdot)$	4011.bv	114	no	$-1$	$1$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{17}{57}\right)$	$e\left(\frac{53}{114}\right)$	$e\left(\frac{18}{19}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{8}{57}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{37}{114}\right)$	$e\left(\frac{101}{114}\right)$
$\chi_{4011}(53,\cdot)$	4011.cj	570	yes	$1$	$1$	$e\left(\frac{523}{570}\right)$	$e\left(\frac{238}{285}\right)$	$e\left(\frac{23}{114}\right)$	$e\left(\frac{143}{190}\right)$	$e\left(\frac{34}{285}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{29}{95}\right)$	$e\left(\frac{191}{285}\right)$	$e\left(\frac{461}{570}\right)$	$e\left(\frac{217}{570}\right)$
$\chi_{4011}(55,\cdot)$	4011.bj	38	no	$1$	$1$	$e\left(\frac{5}{19}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{1}{38}\right)$	$e\left(\frac{15}{19}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{3}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{4}{19}\right)$

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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	$4011$
Structure	\(C_{2}\times C_{2}\times C_{570}\)
Order	$2280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{4011}(1,\cdot)\)	4011.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4011}(2,\cdot)\)	4011.ci	570	yes	\(-1\)	\(1\)	\(e\left(\frac{203}{570}\right)\)	\(e\left(\frac{203}{285}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{13}{190}\right)\)	\(e\left(\frac{29}{285}\right)\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{89}{95}\right)\)	\(e\left(\frac{121}{285}\right)\)	\(e\left(\frac{301}{570}\right)\)	\(e\left(\frac{256}{285}\right)\)
\(\chi_{4011}(4,\cdot)\)	4011.ce	285	no	\(1\)	\(1\)	\(e\left(\frac{203}{285}\right)\)	\(e\left(\frac{121}{285}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{58}{285}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{242}{285}\right)\)	\(e\left(\frac{16}{285}\right)\)	\(e\left(\frac{227}{285}\right)\)
\(\chi_{4011}(5,\cdot)\)	4011.bs	114	yes	\(1\)	\(1\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{49}{114}\right)\)
\(\chi_{4011}(8,\cdot)\)	4011.ca	190	no	\(-1\)	\(1\)	\(e\left(\frac{13}{190}\right)\)	\(e\left(\frac{13}{95}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{39}{190}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{26}{95}\right)\)	\(e\left(\frac{111}{190}\right)\)	\(e\left(\frac{66}{95}\right)\)
\(\chi_{4011}(10,\cdot)\)	4011.cg	570	no	\(-1\)	\(1\)	\(e\left(\frac{29}{285}\right)\)	\(e\left(\frac{58}{285}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{383}{570}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{173}{190}\right)\)	\(e\left(\frac{116}{285}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{187}{570}\right)\)
\(\chi_{4011}(11,\cdot)\)	4011.br	114	yes	\(1\)	\(1\)	\(e\left(\frac{59}{114}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{21}{38}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{89}{114}\right)\)
\(\chi_{4011}(13,\cdot)\)	4011.cc	190	no	\(-1\)	\(1\)	\(e\left(\frac{89}{95}\right)\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{37}{38}\right)\)	\(e\left(\frac{77}{95}\right)\)	\(e\left(\frac{173}{190}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{99}{190}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{51}{190}\right)\)	\(e\left(\frac{17}{190}\right)\)
\(\chi_{4011}(16,\cdot)\)	4011.ce	285	no	\(1\)	\(1\)	\(e\left(\frac{121}{285}\right)\)	\(e\left(\frac{242}{285}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{26}{95}\right)\)	\(e\left(\frac{116}{285}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{199}{285}\right)\)	\(e\left(\frac{32}{285}\right)\)	\(e\left(\frac{169}{285}\right)\)
\(\chi_{4011}(17,\cdot)\)	4011.ck	570	yes	\(1\)	\(1\)	\(e\left(\frac{301}{570}\right)\)	\(e\left(\frac{16}{285}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{111}{190}\right)\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{1}{114}\right)\)	\(e\left(\frac{51}{190}\right)\)	\(e\left(\frac{32}{285}\right)\)	\(e\left(\frac{61}{285}\right)\)	\(e\left(\frac{199}{570}\right)\)
\(\chi_{4011}(19,\cdot)\)	4011.cf	570	no	\(1\)	\(1\)	\(e\left(\frac{256}{285}\right)\)	\(e\left(\frac{227}{285}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{187}{570}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{17}{190}\right)\)	\(e\left(\frac{169}{285}\right)\)	\(e\left(\frac{199}{570}\right)\)	\(e\left(\frac{49}{285}\right)\)
\(\chi_{4011}(20,\cdot)\)	4011.by	190	yes	\(1\)	\(1\)	\(e\left(\frac{87}{190}\right)\)	\(e\left(\frac{87}{95}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{71}{190}\right)\)	\(e\left(\frac{147}{190}\right)\)	\(e\left(\frac{9}{38}\right)\)	\(e\left(\frac{161}{190}\right)\)	\(e\left(\frac{79}{95}\right)\)	\(e\left(\frac{17}{95}\right)\)	\(e\left(\frac{43}{190}\right)\)
\(\chi_{4011}(22,\cdot)\)	4011.cb	190	no	\(-1\)	\(1\)	\(e\left(\frac{83}{95}\right)\)	\(e\left(\frac{71}{95}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{59}{95}\right)\)	\(e\left(\frac{78}{95}\right)\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{4}{95}\right)\)	\(e\left(\frac{47}{95}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{129}{190}\right)\)
\(\chi_{4011}(23,\cdot)\)	4011.ci	570	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{570}\right)\)	\(e\left(\frac{113}{285}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{113}{190}\right)\)	\(e\left(\frac{179}{285}\right)\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{94}{95}\right)\)	\(e\left(\frac{226}{285}\right)\)	\(e\left(\frac{541}{570}\right)\)	\(e\left(\frac{106}{285}\right)\)
\(\chi_{4011}(25,\cdot)\)	4011.bo	57	no	\(1\)	\(1\)	\(e\left(\frac{28}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{9}{19}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{23}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{49}{57}\right)\)
\(\chi_{4011}(26,\cdot)\)	4011.ck	570	yes	\(1\)	\(1\)	\(e\left(\frac{167}{570}\right)\)	\(e\left(\frac{167}{285}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{167}{190}\right)\)	\(e\left(\frac{7}{570}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{87}{190}\right)\)	\(e\left(\frac{49}{285}\right)\)	\(e\left(\frac{227}{285}\right)\)	\(e\left(\frac{563}{570}\right)\)
\(\chi_{4011}(29,\cdot)\)	4011.bz	190	no	\(1\)	\(1\)	\(e\left(\frac{27}{190}\right)\)	\(e\left(\frac{27}{95}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{81}{190}\right)\)	\(e\left(\frac{31}{95}\right)\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{43}{95}\right)\)	\(e\left(\frac{54}{95}\right)\)	\(e\left(\frac{99}{190}\right)\)	\(e\left(\frac{33}{190}\right)\)
\(\chi_{4011}(31,\cdot)\)	4011.bu	114	no	\(1\)	\(1\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{41}{57}\right)\)	\(e\left(\frac{101}{114}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{85}{114}\right)\)	\(e\left(\frac{109}{114}\right)\)	\(e\left(\frac{25}{38}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{43}{57}\right)\)
\(\chi_{4011}(32,\cdot)\)	4011.bq	114	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{114}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{83}{114}\right)\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{67}{114}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(e\left(\frac{28}{57}\right)\)
\(\chi_{4011}(34,\cdot)\)	4011.cc	190	no	\(-1\)	\(1\)	\(e\left(\frac{84}{95}\right)\)	\(e\left(\frac{73}{95}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{62}{95}\right)\)	\(e\left(\frac{143}{190}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{39}{190}\right)\)	\(e\left(\frac{51}{95}\right)\)	\(e\left(\frac{141}{190}\right)\)	\(e\left(\frac{47}{190}\right)\)
\(\chi_{4011}(37,\cdot)\)	4011.bw	114	no	\(-1\)	\(1\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{5}{114}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{85}{114}\right)\)
\(\chi_{4011}(38,\cdot)\)	4011.bt	114	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{49}{114}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)
\(\chi_{4011}(40,\cdot)\)	4011.cg	570	no	\(-1\)	\(1\)	\(e\left(\frac{232}{285}\right)\)	\(e\left(\frac{179}{285}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{42}{95}\right)\)	\(e\left(\frac{499}{570}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{149}{190}\right)\)	\(e\left(\frac{73}{285}\right)\)	\(e\left(\frac{403}{570}\right)\)	\(e\left(\frac{71}{570}\right)\)
\(\chi_{4011}(41,\cdot)\)	4011.bk	38	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{38}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{29}{38}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{4011}(43,\cdot)\)	4011.bp	95	no	\(1\)	\(1\)	\(e\left(\frac{81}{95}\right)\)	\(e\left(\frac{67}{95}\right)\)	\(e\left(\frac{2}{19}\right)\)	\(e\left(\frac{53}{95}\right)\)	\(e\left(\frac{91}{95}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{68}{95}\right)\)	\(e\left(\frac{39}{95}\right)\)	\(e\left(\frac{12}{95}\right)\)	\(e\left(\frac{4}{95}\right)\)
\(\chi_{4011}(44,\cdot)\)	4011.cj	570	yes	\(1\)	\(1\)	\(e\left(\frac{131}{570}\right)\)	\(e\left(\frac{131}{285}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{131}{190}\right)\)	\(e\left(\frac{263}{285}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{93}{95}\right)\)	\(e\left(\frac{262}{285}\right)\)	\(e\left(\frac{37}{570}\right)\)	\(e\left(\frac{329}{570}\right)\)
\(\chi_{4011}(46,\cdot)\)	4011.ce	285	no	\(1\)	\(1\)	\(e\left(\frac{158}{285}\right)\)	\(e\left(\frac{31}{285}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{63}{95}\right)\)	\(e\left(\frac{208}{285}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{88}{95}\right)\)	\(e\left(\frac{62}{285}\right)\)	\(e\left(\frac{136}{285}\right)\)	\(e\left(\frac{77}{285}\right)\)
\(\chi_{4011}(47,\cdot)\)	4011.cl	570	yes	\(-1\)	\(1\)	\(e\left(\frac{371}{570}\right)\)	\(e\left(\frac{86}{285}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{181}{190}\right)\)	\(e\left(\frac{391}{570}\right)\)	\(e\left(\frac{49}{57}\right)\)	\(e\left(\frac{1}{190}\right)\)	\(e\left(\frac{172}{285}\right)\)	\(e\left(\frac{221}{285}\right)\)	\(e\left(\frac{232}{285}\right)\)
\(\chi_{4011}(50,\cdot)\)	4011.ca	190	no	\(-1\)	\(1\)	\(e\left(\frac{161}{190}\right)\)	\(e\left(\frac{66}{95}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{103}{190}\right)\)	\(e\left(\frac{23}{95}\right)\)	\(e\left(\frac{35}{38}\right)\)	\(e\left(\frac{84}{95}\right)\)	\(e\left(\frac{37}{95}\right)\)	\(e\left(\frac{147}{190}\right)\)	\(e\left(\frac{72}{95}\right)\)
\(\chi_{4011}(52,\cdot)\)	4011.bv	114	no	\(-1\)	\(1\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{17}{57}\right)\)	\(e\left(\frac{53}{114}\right)\)	\(e\left(\frac{18}{19}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{8}{57}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{37}{114}\right)\)	\(e\left(\frac{101}{114}\right)\)
\(\chi_{4011}(53,\cdot)\)	4011.cj	570	yes	\(1\)	\(1\)	\(e\left(\frac{523}{570}\right)\)	\(e\left(\frac{238}{285}\right)\)	\(e\left(\frac{23}{114}\right)\)	\(e\left(\frac{143}{190}\right)\)	\(e\left(\frac{34}{285}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{29}{95}\right)\)	\(e\left(\frac{191}{285}\right)\)	\(e\left(\frac{461}{570}\right)\)	\(e\left(\frac{217}{570}\right)\)
\(\chi_{4011}(55,\cdot)\)	4011.bj	38	no	\(1\)	\(1\)	\(e\left(\frac{5}{19}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{1}{38}\right)\)	\(e\left(\frac{15}{19}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{3}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{4}{19}\right)\)

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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.