LMFDB - Group of Dirichlet characters of modulus 6028

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6028)

pari: g = idealstar(,6028,2)

Character group

sage: G.order() pari: g.no
Order	=	2720
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{680}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6028}(3015,\cdot)$, $\chi_{6028}(2741,\cdot)$, $\chi_{6028}(3565,\cdot)$

First 32 of 2720 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{6028}(1,\cdot)$	6028.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6028}(3,\cdot)$	6028.cl	680	yes	$1$	$1$	$e\left(\frac{617}{680}\right)$	$e\left(\frac{511}{680}\right)$	$e\left(\frac{139}{340}\right)$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{669}{680}\right)$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{163}{340}\right)$	$e\left(\frac{81}{340}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{57}{136}\right)$
$\chi_{6028}(5,\cdot)$	6028.ci	680	no	$-1$	$1$	$e\left(\frac{511}{680}\right)$	$e\left(\frac{653}{680}\right)$	$e\left(\frac{327}{340}\right)$	$e\left(\frac{171}{340}\right)$	$e\left(\frac{127}{680}\right)$	$e\left(\frac{121}{170}\right)$	$e\left(\frac{189}{340}\right)$	$e\left(\frac{193}{340}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{127}{136}\right)$
$\chi_{6028}(7,\cdot)$	6028.ce	340	yes	$1$	$1$	$e\left(\frac{139}{340}\right)$	$e\left(\frac{327}{340}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{139}{170}\right)$	$e\left(\frac{143}{340}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{137}{170}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{7}{68}\right)$
$\chi_{6028}(9,\cdot)$	6028.cf	340	no	$1$	$1$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{171}{340}\right)$	$e\left(\frac{139}{170}\right)$	$e\left(\frac{107}{170}\right)$	$e\left(\frac{329}{340}\right)$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{163}{170}\right)$	$e\left(\frac{81}{170}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{6028}(13,\cdot)$	6028.cj	680	no	$1$	$1$	$e\left(\frac{669}{680}\right)$	$e\left(\frac{127}{680}\right)$	$e\left(\frac{143}{340}\right)$	$e\left(\frac{329}{340}\right)$	$e\left(\frac{473}{680}\right)$	$e\left(\frac{29}{170}\right)$	$e\left(\frac{301}{340}\right)$	$e\left(\frac{257}{340}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{133}{136}\right)$
$\chi_{6028}(15,\cdot)$	6028.cb	170	yes	$-1$	$1$	$e\left(\frac{56}{85}\right)$	$e\left(\frac{121}{170}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{29}{170}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{137}{170}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{6}{17}\right)$
$\chi_{6028}(17,\cdot)$	6028.ch	340	no	$-1$	$1$	$e\left(\frac{163}{340}\right)$	$e\left(\frac{189}{340}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{163}{170}\right)$	$e\left(\frac{301}{340}\right)$	$e\left(\frac{3}{85}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{63}{68}\right)$
$\chi_{6028}(19,\cdot)$	6028.ce	340	yes	$1$	$1$	$e\left(\frac{81}{340}\right)$	$e\left(\frac{193}{340}\right)$	$e\left(\frac{137}{170}\right)$	$e\left(\frac{81}{170}\right)$	$e\left(\frac{257}{340}\right)$	$e\left(\frac{137}{170}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{163}{170}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{53}{68}\right)$
$\chi_{6028}(21,\cdot)$	6028.bv	136	no	$1$	$1$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{55}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{71}{136}\right)$
$\chi_{6028}(23,\cdot)$	6028.bt	136	no	$1$	$1$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{133}{136}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{71}{136}\right)$	$e\left(\frac{53}{136}\right)$
$\chi_{6028}(25,\cdot)$	6028.cf	340	no	$1$	$1$	$e\left(\frac{171}{340}\right)$	$e\left(\frac{313}{340}\right)$	$e\left(\frac{157}{170}\right)$	$e\left(\frac{1}{170}\right)$	$e\left(\frac{127}{340}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{19}{170}\right)$	$e\left(\frac{23}{170}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{59}{68}\right)$
$\chi_{6028}(27,\cdot)$	6028.cl	680	yes	$1$	$1$	$e\left(\frac{491}{680}\right)$	$e\left(\frac{173}{680}\right)$	$e\left(\frac{77}{340}\right)$	$e\left(\frac{151}{340}\right)$	$e\left(\frac{647}{680}\right)$	$e\left(\frac{83}{85}\right)$	$e\left(\frac{149}{340}\right)$	$e\left(\frac{243}{340}\right)$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{35}{136}\right)$
$\chi_{6028}(29,\cdot)$	6028.cj	680	no	$1$	$1$	$e\left(\frac{183}{680}\right)$	$e\left(\frac{669}{680}\right)$	$e\left(\frac{1}{340}\right)$	$e\left(\frac{183}{340}\right)$	$e\left(\frac{291}{680}\right)$	$e\left(\frac{43}{170}\right)$	$e\left(\frac{247}{340}\right)$	$e\left(\frac{299}{340}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{87}{136}\right)$
$\chi_{6028}(31,\cdot)$	6028.cl	680	yes	$1$	$1$	$e\left(\frac{569}{680}\right)$	$e\left(\frac{447}{680}\right)$	$e\left(\frac{83}{340}\right)$	$e\left(\frac{229}{340}\right)$	$e\left(\frac{13}{680}\right)$	$e\left(\frac{42}{85}\right)$	$e\left(\frac{271}{340}\right)$	$e\left(\frac{337}{340}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{81}{136}\right)$
$\chi_{6028}(35,\cdot)$	6028.ck	680	yes	$-1$	$1$	$e\left(\frac{109}{680}\right)$	$e\left(\frac{627}{680}\right)$	$e\left(\frac{113}{340}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{413}{680}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{201}{340}\right)$	$e\left(\frac{127}{340}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{5}{136}\right)$
$\chi_{6028}(37,\cdot)$	6028.bb	20	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$-i$
$\chi_{6028}(39,\cdot)$	6028.ce	340	yes	$1$	$1$	$e\left(\frac{303}{340}\right)$	$e\left(\frac{319}{340}\right)$	$e\left(\frac{141}{170}\right)$	$e\left(\frac{133}{170}\right)$	$e\left(\frac{231}{340}\right)$	$e\left(\frac{141}{170}\right)$	$e\left(\frac{31}{85}\right)$	$e\left(\frac{169}{170}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{6028}(41,\cdot)$	6028.bm	40	no	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{6028}(43,\cdot)$	6028.bu	136	yes	$-1$	$1$	$e\left(\frac{29}{136}\right)$	$e\left(\frac{67}{136}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{23}{136}\right)$	$e\left(\frac{89}{136}\right)$
$\chi_{6028}(45,\cdot)$	6028.bw	136	no	$-1$	$1$	$e\left(\frac{77}{136}\right)$	$e\left(\frac{63}{136}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{47}{136}\right)$	$e\left(\frac{105}{136}\right)$
$\chi_{6028}(47,\cdot)$	6028.cl	680	yes	$1$	$1$	$e\left(\frac{27}{680}\right)$	$e\left(\frac{461}{680}\right)$	$e\left(\frac{329}{340}\right)$	$e\left(\frac{27}{340}\right)$	$e\left(\frac{199}{680}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{173}{340}\right)$	$e\left(\frac{111}{340}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{131}{136}\right)$
$\chi_{6028}(49,\cdot)$	6028.by	170	no	$1$	$1$	$e\left(\frac{139}{170}\right)$	$e\left(\frac{157}{170}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{54}{85}\right)$	$e\left(\frac{143}{170}\right)$	$e\left(\frac{63}{85}\right)$	$e\left(\frac{6}{85}\right)$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{7}{34}\right)$
$\chi_{6028}(51,\cdot)$	6028.ck	680	yes	$-1$	$1$	$e\left(\frac{263}{680}\right)$	$e\left(\frac{209}{680}\right)$	$e\left(\frac{151}{340}\right)$	$e\left(\frac{263}{340}\right)$	$e\left(\frac{591}{680}\right)$	$e\left(\frac{59}{85}\right)$	$e\left(\frac{67}{340}\right)$	$e\left(\frac{269}{340}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{47}{136}\right)$
$\chi_{6028}(53,\cdot)$	6028.ci	680	no	$-1$	$1$	$e\left(\frac{519}{680}\right)$	$e\left(\frac{437}{680}\right)$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{179}{340}\right)$	$e\left(\frac{463}{680}\right)$	$e\left(\frac{69}{170}\right)$	$e\left(\frac{1}{340}\right)$	$e\left(\frac{37}{340}\right)$	$e\left(\frac{57}{136}\right)$	$e\left(\frac{55}{136}\right)$
$\chi_{6028}(57,\cdot)$	6028.cj	680	no	$1$	$1$	$e\left(\frac{99}{680}\right)$	$e\left(\frac{217}{680}\right)$	$e\left(\frac{73}{340}\right)$	$e\left(\frac{99}{340}\right)$	$e\left(\frac{503}{680}\right)$	$e\left(\frac{79}{170}\right)$	$e\left(\frac{11}{340}\right)$	$e\left(\frac{67}{340}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{27}{136}\right)$
$\chi_{6028}(59,\cdot)$	6028.bz	170	yes	$-1$	$1$	$e\left(\frac{147}{170}\right)$	$e\left(\frac{13}{85}\right)$	$e\left(\frac{3}{170}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{27}{85}\right)$	$e\left(\frac{3}{170}\right)$	$e\left(\frac{73}{85}\right)$	$e\left(\frac{47}{170}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{6028}(61,\cdot)$	6028.ch	340	no	$-1$	$1$	$e\left(\frac{63}{340}\right)$	$e\left(\frac{169}{340}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{63}{170}\right)$	$e\left(\frac{181}{340}\right)$	$e\left(\frac{58}{85}\right)$	$e\left(\frac{46}{85}\right)$	$e\left(\frac{2}{85}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{11}{68}\right)$
$\chi_{6028}(63,\cdot)$	6028.cc	170	yes	$1$	$1$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{79}{170}\right)$	$e\left(\frac{16}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{33}{85}\right)$	$e\left(\frac{117}{170}\right)$	$e\left(\frac{169}{170}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{16}{17}\right)$
$\chi_{6028}(65,\cdot)$	6028.bj	34	no	$-1$	$1$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{31}{34}\right)$
$\chi_{6028}(67,\cdot)$	6028.bt	136	no	$1$	$1$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{6028}(69,\cdot)$	6028.cf	340	no	$1$	$1$	$e\left(\frac{111}{340}\right)$	$e\left(\frac{233}{340}\right)$	$e\left(\frac{87}{170}\right)$	$e\left(\frac{111}{170}\right)$	$e\left(\frac{327}{340}\right)$	$e\left(\frac{1}{85}\right)$	$e\left(\frac{69}{170}\right)$	$e\left(\frac{3}{170}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{55}{68}\right)$

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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	$6028$
Structure	\(C_{2}\times C_{2}\times C_{680}\)
Order	$2720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{6028}(1,\cdot)\)	6028.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6028}(3,\cdot)\)	6028.cl	680	yes	\(1\)	\(1\)	\(e\left(\frac{617}{680}\right)\)	\(e\left(\frac{511}{680}\right)\)	\(e\left(\frac{139}{340}\right)\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{669}{680}\right)\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{163}{340}\right)\)	\(e\left(\frac{81}{340}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{57}{136}\right)\)
\(\chi_{6028}(5,\cdot)\)	6028.ci	680	no	\(-1\)	\(1\)	\(e\left(\frac{511}{680}\right)\)	\(e\left(\frac{653}{680}\right)\)	\(e\left(\frac{327}{340}\right)\)	\(e\left(\frac{171}{340}\right)\)	\(e\left(\frac{127}{680}\right)\)	\(e\left(\frac{121}{170}\right)\)	\(e\left(\frac{189}{340}\right)\)	\(e\left(\frac{193}{340}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{127}{136}\right)\)
\(\chi_{6028}(7,\cdot)\)	6028.ce	340	yes	\(1\)	\(1\)	\(e\left(\frac{139}{340}\right)\)	\(e\left(\frac{327}{340}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{139}{170}\right)\)	\(e\left(\frac{143}{340}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{137}{170}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)
\(\chi_{6028}(9,\cdot)\)	6028.cf	340	no	\(1\)	\(1\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{171}{340}\right)\)	\(e\left(\frac{139}{170}\right)\)	\(e\left(\frac{107}{170}\right)\)	\(e\left(\frac{329}{340}\right)\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{163}{170}\right)\)	\(e\left(\frac{81}{170}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{6028}(13,\cdot)\)	6028.cj	680	no	\(1\)	\(1\)	\(e\left(\frac{669}{680}\right)\)	\(e\left(\frac{127}{680}\right)\)	\(e\left(\frac{143}{340}\right)\)	\(e\left(\frac{329}{340}\right)\)	\(e\left(\frac{473}{680}\right)\)	\(e\left(\frac{29}{170}\right)\)	\(e\left(\frac{301}{340}\right)\)	\(e\left(\frac{257}{340}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{133}{136}\right)\)
\(\chi_{6028}(15,\cdot)\)	6028.cb	170	yes	\(-1\)	\(1\)	\(e\left(\frac{56}{85}\right)\)	\(e\left(\frac{121}{170}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{29}{170}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{137}{170}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)
\(\chi_{6028}(17,\cdot)\)	6028.ch	340	no	\(-1\)	\(1\)	\(e\left(\frac{163}{340}\right)\)	\(e\left(\frac{189}{340}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{163}{170}\right)\)	\(e\left(\frac{301}{340}\right)\)	\(e\left(\frac{3}{85}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{63}{68}\right)\)
\(\chi_{6028}(19,\cdot)\)	6028.ce	340	yes	\(1\)	\(1\)	\(e\left(\frac{81}{340}\right)\)	\(e\left(\frac{193}{340}\right)\)	\(e\left(\frac{137}{170}\right)\)	\(e\left(\frac{81}{170}\right)\)	\(e\left(\frac{257}{340}\right)\)	\(e\left(\frac{137}{170}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{163}{170}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)
\(\chi_{6028}(21,\cdot)\)	6028.bv	136	no	\(1\)	\(1\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{55}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{71}{136}\right)\)
\(\chi_{6028}(23,\cdot)\)	6028.bt	136	no	\(1\)	\(1\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{133}{136}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{71}{136}\right)\)	\(e\left(\frac{53}{136}\right)\)
\(\chi_{6028}(25,\cdot)\)	6028.cf	340	no	\(1\)	\(1\)	\(e\left(\frac{171}{340}\right)\)	\(e\left(\frac{313}{340}\right)\)	\(e\left(\frac{157}{170}\right)\)	\(e\left(\frac{1}{170}\right)\)	\(e\left(\frac{127}{340}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{19}{170}\right)\)	\(e\left(\frac{23}{170}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)
\(\chi_{6028}(27,\cdot)\)	6028.cl	680	yes	\(1\)	\(1\)	\(e\left(\frac{491}{680}\right)\)	\(e\left(\frac{173}{680}\right)\)	\(e\left(\frac{77}{340}\right)\)	\(e\left(\frac{151}{340}\right)\)	\(e\left(\frac{647}{680}\right)\)	\(e\left(\frac{83}{85}\right)\)	\(e\left(\frac{149}{340}\right)\)	\(e\left(\frac{243}{340}\right)\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{35}{136}\right)\)
\(\chi_{6028}(29,\cdot)\)	6028.cj	680	no	\(1\)	\(1\)	\(e\left(\frac{183}{680}\right)\)	\(e\left(\frac{669}{680}\right)\)	\(e\left(\frac{1}{340}\right)\)	\(e\left(\frac{183}{340}\right)\)	\(e\left(\frac{291}{680}\right)\)	\(e\left(\frac{43}{170}\right)\)	\(e\left(\frac{247}{340}\right)\)	\(e\left(\frac{299}{340}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{87}{136}\right)\)
\(\chi_{6028}(31,\cdot)\)	6028.cl	680	yes	\(1\)	\(1\)	\(e\left(\frac{569}{680}\right)\)	\(e\left(\frac{447}{680}\right)\)	\(e\left(\frac{83}{340}\right)\)	\(e\left(\frac{229}{340}\right)\)	\(e\left(\frac{13}{680}\right)\)	\(e\left(\frac{42}{85}\right)\)	\(e\left(\frac{271}{340}\right)\)	\(e\left(\frac{337}{340}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{81}{136}\right)\)
\(\chi_{6028}(35,\cdot)\)	6028.ck	680	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{680}\right)\)	\(e\left(\frac{627}{680}\right)\)	\(e\left(\frac{113}{340}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{413}{680}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{201}{340}\right)\)	\(e\left(\frac{127}{340}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{5}{136}\right)\)
\(\chi_{6028}(37,\cdot)\)	6028.bb	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(-i\)
\(\chi_{6028}(39,\cdot)\)	6028.ce	340	yes	\(1\)	\(1\)	\(e\left(\frac{303}{340}\right)\)	\(e\left(\frac{319}{340}\right)\)	\(e\left(\frac{141}{170}\right)\)	\(e\left(\frac{133}{170}\right)\)	\(e\left(\frac{231}{340}\right)\)	\(e\left(\frac{141}{170}\right)\)	\(e\left(\frac{31}{85}\right)\)	\(e\left(\frac{169}{170}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{6028}(41,\cdot)\)	6028.bm	40	no	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{6028}(43,\cdot)\)	6028.bu	136	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{136}\right)\)	\(e\left(\frac{67}{136}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{23}{136}\right)\)	\(e\left(\frac{89}{136}\right)\)
\(\chi_{6028}(45,\cdot)\)	6028.bw	136	no	\(-1\)	\(1\)	\(e\left(\frac{77}{136}\right)\)	\(e\left(\frac{63}{136}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{47}{136}\right)\)	\(e\left(\frac{105}{136}\right)\)
\(\chi_{6028}(47,\cdot)\)	6028.cl	680	yes	\(1\)	\(1\)	\(e\left(\frac{27}{680}\right)\)	\(e\left(\frac{461}{680}\right)\)	\(e\left(\frac{329}{340}\right)\)	\(e\left(\frac{27}{340}\right)\)	\(e\left(\frac{199}{680}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{173}{340}\right)\)	\(e\left(\frac{111}{340}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{131}{136}\right)\)
\(\chi_{6028}(49,\cdot)\)	6028.by	170	no	\(1\)	\(1\)	\(e\left(\frac{139}{170}\right)\)	\(e\left(\frac{157}{170}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{54}{85}\right)\)	\(e\left(\frac{143}{170}\right)\)	\(e\left(\frac{63}{85}\right)\)	\(e\left(\frac{6}{85}\right)\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)
\(\chi_{6028}(51,\cdot)\)	6028.ck	680	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{680}\right)\)	\(e\left(\frac{209}{680}\right)\)	\(e\left(\frac{151}{340}\right)\)	\(e\left(\frac{263}{340}\right)\)	\(e\left(\frac{591}{680}\right)\)	\(e\left(\frac{59}{85}\right)\)	\(e\left(\frac{67}{340}\right)\)	\(e\left(\frac{269}{340}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{47}{136}\right)\)
\(\chi_{6028}(53,\cdot)\)	6028.ci	680	no	\(-1\)	\(1\)	\(e\left(\frac{519}{680}\right)\)	\(e\left(\frac{437}{680}\right)\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{179}{340}\right)\)	\(e\left(\frac{463}{680}\right)\)	\(e\left(\frac{69}{170}\right)\)	\(e\left(\frac{1}{340}\right)\)	\(e\left(\frac{37}{340}\right)\)	\(e\left(\frac{57}{136}\right)\)	\(e\left(\frac{55}{136}\right)\)
\(\chi_{6028}(57,\cdot)\)	6028.cj	680	no	\(1\)	\(1\)	\(e\left(\frac{99}{680}\right)\)	\(e\left(\frac{217}{680}\right)\)	\(e\left(\frac{73}{340}\right)\)	\(e\left(\frac{99}{340}\right)\)	\(e\left(\frac{503}{680}\right)\)	\(e\left(\frac{79}{170}\right)\)	\(e\left(\frac{11}{340}\right)\)	\(e\left(\frac{67}{340}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{27}{136}\right)\)
\(\chi_{6028}(59,\cdot)\)	6028.bz	170	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{170}\right)\)	\(e\left(\frac{13}{85}\right)\)	\(e\left(\frac{3}{170}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{27}{85}\right)\)	\(e\left(\frac{3}{170}\right)\)	\(e\left(\frac{73}{85}\right)\)	\(e\left(\frac{47}{170}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{6028}(61,\cdot)\)	6028.ch	340	no	\(-1\)	\(1\)	\(e\left(\frac{63}{340}\right)\)	\(e\left(\frac{169}{340}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{63}{170}\right)\)	\(e\left(\frac{181}{340}\right)\)	\(e\left(\frac{58}{85}\right)\)	\(e\left(\frac{46}{85}\right)\)	\(e\left(\frac{2}{85}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)
\(\chi_{6028}(63,\cdot)\)	6028.cc	170	yes	\(1\)	\(1\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{79}{170}\right)\)	\(e\left(\frac{16}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{33}{85}\right)\)	\(e\left(\frac{117}{170}\right)\)	\(e\left(\frac{169}{170}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)
\(\chi_{6028}(65,\cdot)\)	6028.bj	34	no	\(-1\)	\(1\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{6028}(67,\cdot)\)	6028.bt	136	no	\(1\)	\(1\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{6028}(69,\cdot)\)	6028.cf	340	no	\(1\)	\(1\)	\(e\left(\frac{111}{340}\right)\)	\(e\left(\frac{233}{340}\right)\)	\(e\left(\frac{87}{170}\right)\)	\(e\left(\frac{111}{170}\right)\)	\(e\left(\frac{327}{340}\right)\)	\(e\left(\frac{1}{85}\right)\)	\(e\left(\frac{69}{170}\right)\)	\(e\left(\frac{3}{170}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)

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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.