LMFDB - Group of Dirichlet characters of modulus 6069

sage:H = DirichletGroup(6069)

pari:g = idealstar(,6069,2)

Character group

sage:G.order() pari:g.no
Order	=	3264
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{816}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{6069}(2024,\cdot)$, $\chi_{6069}(4336,\cdot)$, $\chi_{6069}(3760,\cdot)$

First 32 of 3264 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$19$	$20$
$\chi_{6069}(1,\cdot)$	6069.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6069}(2,\cdot)$	6069.cw	408	yes	$-1$	$1$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{53}{408}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{367}{408}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{123}{136}\right)$
$\chi_{6069}(4,\cdot)$	6069.cm	204	no	$1$	$1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{6069}(5,\cdot)$	6069.cy	816	yes	$-1$	$1$	$e\left(\frac{53}{408}\right)$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{379}{816}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{485}{816}\right)$	$e\left(\frac{161}{816}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{197}{272}\right)$
$\chi_{6069}(8,\cdot)$	6069.cl	136	no	$-1$	$1$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{97}{136}\right)$
$\chi_{6069}(10,\cdot)$	6069.da	816	no	$1$	$1$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{485}{816}\right)$	$e\left(\frac{7}{136}\right)$	$e\left(\frac{499}{816}\right)$	$e\left(\frac{79}{816}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{171}{272}\right)$
$\chi_{6069}(11,\cdot)$	6069.cz	816	yes	$1$	$1$	$e\left(\frac{367}{408}\right)$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{161}{816}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{79}{816}\right)$	$e\left(\frac{91}{816}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{271}{272}\right)$
$\chi_{6069}(13,\cdot)$	6069.ca	68	no	$-1$	$1$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{23}{68}\right)$
$\chi_{6069}(16,\cdot)$	6069.cf	102	no	$1$	$1$	$e\left(\frac{28}{51}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{21}{34}\right)$
$\chi_{6069}(19,\cdot)$	6069.cu	408	no	$-1$	$1$	$e\left(\frac{91}{204}\right)$	$e\left(\frac{91}{102}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{211}{408}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{40}{51}\right)$	$e\left(\frac{181}{204}\right)$	$e\left(\frac{115}{136}\right)$
$\chi_{6069}(20,\cdot)$	6069.cr	272	yes	$-1$	$1$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{197}{272}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{171}{272}\right)$	$e\left(\frac{271}{272}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{145}{272}\right)$
$\chi_{6069}(22,\cdot)$	6069.cs	272	no	$-1$	$1$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{89}{272}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{31}{272}\right)$	$e\left(\frac{3}{272}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{131}{136}\right)$	$e\left(\frac{245}{272}\right)$
$\chi_{6069}(23,\cdot)$	6069.cz	816	yes	$1$	$1$	$e\left(\frac{383}{408}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{745}{816}\right)$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{695}{816}\right)$	$e\left(\frac{563}{816}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{77}{102}\right)$	$e\left(\frac{59}{408}\right)$	$e\left(\frac{215}{272}\right)$
$\chi_{6069}(25,\cdot)$	6069.cx	408	no	$1$	$1$	$e\left(\frac{53}{204}\right)$	$e\left(\frac{53}{102}\right)$	$e\left(\frac{379}{408}\right)$	$e\left(\frac{53}{68}\right)$	$e\left(\frac{77}{408}\right)$	$e\left(\frac{161}{408}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{61}{136}\right)$
$\chi_{6069}(26,\cdot)$	6069.cv	408	yes	$1$	$1$	$e\left(\frac{163}{204}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{181}{408}\right)$	$e\left(\frac{193}{408}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{7}{204}\right)$	$e\left(\frac{33}{136}\right)$
$\chi_{6069}(29,\cdot)$	6069.cq	272	no	$1$	$1$	$e\left(\frac{111}{136}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{201}{272}\right)$	$e\left(\frac{61}{136}\right)$	$e\left(\frac{151}{272}\right)$	$e\left(\frac{19}{272}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{101}{272}\right)$
$\chi_{6069}(31,\cdot)$	6069.da	816	no	$1$	$1$	$e\left(\frac{253}{408}\right)$	$e\left(\frac{49}{204}\right)$	$e\left(\frac{335}{816}\right)$	$e\left(\frac{117}{136}\right)$	$e\left(\frac{25}{816}\right)$	$e\left(\frac{349}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{121}{408}\right)$	$e\left(\frac{177}{272}\right)$
$\chi_{6069}(32,\cdot)$	6069.cw	408	yes	$-1$	$1$	$e\left(\frac{89}{204}\right)$	$e\left(\frac{89}{102}\right)$	$e\left(\frac{265}{408}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{35}{408}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{47}{204}\right)$	$e\left(\frac{71}{136}\right)$
$\chi_{6069}(37,\cdot)$	6069.db	816	no	$-1$	$1$	$e\left(\frac{317}{408}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{223}{816}\right)$	$e\left(\frac{45}{136}\right)$	$e\left(\frac{41}{816}\right)$	$e\left(\frac{197}{816}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{11}{102}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{225}{272}\right)$
$\chi_{6069}(38,\cdot)$	6069.y	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$
$\chi_{6069}(40,\cdot)$	6069.bt	48	no	$1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{43}{48}\right)$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{6069}(41,\cdot)$	6069.cr	272	yes	$-1$	$1$	$e\left(\frac{129}{136}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{263}{272}\right)$	$e\left(\frac{115}{136}\right)$	$e\left(\frac{249}{272}\right)$	$e\left(\frac{261}{272}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{235}{272}\right)$
$\chi_{6069}(43,\cdot)$	6069.ck	136	no	$1$	$1$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{37}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{19}{136}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{1}{136}\right)$
$\chi_{6069}(44,\cdot)$	6069.cz	816	yes	$1$	$1$	$e\left(\frac{275}{408}\right)$	$e\left(\frac{71}{204}\right)$	$e\left(\frac{373}{816}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{107}{816}\right)$	$e\left(\frac{743}{816}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{71}{102}\right)$	$e\left(\frac{167}{408}\right)$	$e\left(\frac{219}{272}\right)$
$\chi_{6069}(46,\cdot)$	6069.db	816	no	$-1$	$1$	$e\left(\frac{337}{408}\right)$	$e\left(\frac{133}{204}\right)$	$e\left(\frac{35}{816}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{709}{816}\right)$	$e\left(\frac{481}{816}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{241}{408}\right)$	$e\left(\frac{189}{272}\right)$
$\chi_{6069}(47,\cdot)$	6069.cp	204	yes	$1$	$1$	$e\left(\frac{1}{51}\right)$	$e\left(\frac{2}{51}\right)$	$e\left(\frac{175}{204}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{4}{51}\right)$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{61}{68}\right)$
$\chi_{6069}(50,\cdot)$	6069.bo	34	no	$-1$	$1$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{6}{17}\right)$
$\chi_{6069}(52,\cdot)$	6069.cg	102	no	$-1$	$1$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{19}{51}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{38}{51}\right)$	$e\left(\frac{49}{102}\right)$	$e\left(\frac{5}{34}\right)$
$\chi_{6069}(53,\cdot)$	6069.cw	408	yes	$-1$	$1$	$e\left(\frac{149}{204}\right)$	$e\left(\frac{47}{102}\right)$	$e\left(\frac{109}{408}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{407}{408}\right)$	$e\left(\frac{239}{408}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{47}{51}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{99}{136}\right)$
$\chi_{6069}(55,\cdot)$	6069.ca	68	no	$-1$	$1$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{49}{68}\right)$
$\chi_{6069}(58,\cdot)$	6069.db	816	no	$-1$	$1$	$e\left(\frac{287}{408}\right)$	$e\left(\frac{83}{204}\right)$	$e\left(\frac{709}{816}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{467}{816}\right)$	$e\left(\frac{791}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{359}{408}\right)$	$e\left(\frac{75}{272}\right)$
$\chi_{6069}(59,\cdot)$	6069.cv	408	yes	$1$	$1$	$e\left(\frac{59}{204}\right)$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{139}{408}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{257}{408}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{8}{51}\right)$	$e\left(\frac{179}{204}\right)$	$e\left(\frac{125}{136}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$6069$
Structure	\(C_{2}\times C_{2}\times C_{816}\)
Order	$3264$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(19\)	\(20\)
\(\chi_{6069}(1,\cdot)\)	6069.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6069}(2,\cdot)\)	6069.cw	408	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{53}{408}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{367}{408}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{123}{136}\right)\)
\(\chi_{6069}(4,\cdot)\)	6069.cm	204	no	\(1\)	\(1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{6069}(5,\cdot)\)	6069.cy	816	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{408}\right)\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{379}{816}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{485}{816}\right)\)	\(e\left(\frac{161}{816}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{197}{272}\right)\)
\(\chi_{6069}(8,\cdot)\)	6069.cl	136	no	\(-1\)	\(1\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)
\(\chi_{6069}(10,\cdot)\)	6069.da	816	no	\(1\)	\(1\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{485}{816}\right)\)	\(e\left(\frac{7}{136}\right)\)	\(e\left(\frac{499}{816}\right)\)	\(e\left(\frac{79}{816}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{171}{272}\right)\)
\(\chi_{6069}(11,\cdot)\)	6069.cz	816	yes	\(1\)	\(1\)	\(e\left(\frac{367}{408}\right)\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{161}{816}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{79}{816}\right)\)	\(e\left(\frac{91}{816}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{271}{272}\right)\)
\(\chi_{6069}(13,\cdot)\)	6069.ca	68	no	\(-1\)	\(1\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)
\(\chi_{6069}(16,\cdot)\)	6069.cf	102	no	\(1\)	\(1\)	\(e\left(\frac{28}{51}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{6069}(19,\cdot)\)	6069.cu	408	no	\(-1\)	\(1\)	\(e\left(\frac{91}{204}\right)\)	\(e\left(\frac{91}{102}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{211}{408}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{40}{51}\right)\)	\(e\left(\frac{181}{204}\right)\)	\(e\left(\frac{115}{136}\right)\)
\(\chi_{6069}(20,\cdot)\)	6069.cr	272	yes	\(-1\)	\(1\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{197}{272}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{171}{272}\right)\)	\(e\left(\frac{271}{272}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{145}{272}\right)\)
\(\chi_{6069}(22,\cdot)\)	6069.cs	272	no	\(-1\)	\(1\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{89}{272}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{31}{272}\right)\)	\(e\left(\frac{3}{272}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{131}{136}\right)\)	\(e\left(\frac{245}{272}\right)\)
\(\chi_{6069}(23,\cdot)\)	6069.cz	816	yes	\(1\)	\(1\)	\(e\left(\frac{383}{408}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{745}{816}\right)\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{695}{816}\right)\)	\(e\left(\frac{563}{816}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{77}{102}\right)\)	\(e\left(\frac{59}{408}\right)\)	\(e\left(\frac{215}{272}\right)\)
\(\chi_{6069}(25,\cdot)\)	6069.cx	408	no	\(1\)	\(1\)	\(e\left(\frac{53}{204}\right)\)	\(e\left(\frac{53}{102}\right)\)	\(e\left(\frac{379}{408}\right)\)	\(e\left(\frac{53}{68}\right)\)	\(e\left(\frac{77}{408}\right)\)	\(e\left(\frac{161}{408}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{61}{136}\right)\)
\(\chi_{6069}(26,\cdot)\)	6069.cv	408	yes	\(1\)	\(1\)	\(e\left(\frac{163}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{181}{408}\right)\)	\(e\left(\frac{193}{408}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{7}{204}\right)\)	\(e\left(\frac{33}{136}\right)\)
\(\chi_{6069}(29,\cdot)\)	6069.cq	272	no	\(1\)	\(1\)	\(e\left(\frac{111}{136}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{201}{272}\right)\)	\(e\left(\frac{61}{136}\right)\)	\(e\left(\frac{151}{272}\right)\)	\(e\left(\frac{19}{272}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{101}{272}\right)\)
\(\chi_{6069}(31,\cdot)\)	6069.da	816	no	\(1\)	\(1\)	\(e\left(\frac{253}{408}\right)\)	\(e\left(\frac{49}{204}\right)\)	\(e\left(\frac{335}{816}\right)\)	\(e\left(\frac{117}{136}\right)\)	\(e\left(\frac{25}{816}\right)\)	\(e\left(\frac{349}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{121}{408}\right)\)	\(e\left(\frac{177}{272}\right)\)
\(\chi_{6069}(32,\cdot)\)	6069.cw	408	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{204}\right)\)	\(e\left(\frac{89}{102}\right)\)	\(e\left(\frac{265}{408}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{35}{408}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{47}{204}\right)\)	\(e\left(\frac{71}{136}\right)\)
\(\chi_{6069}(37,\cdot)\)	6069.db	816	no	\(-1\)	\(1\)	\(e\left(\frac{317}{408}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{223}{816}\right)\)	\(e\left(\frac{45}{136}\right)\)	\(e\left(\frac{41}{816}\right)\)	\(e\left(\frac{197}{816}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{11}{102}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{225}{272}\right)\)
\(\chi_{6069}(38,\cdot)\)	6069.y	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)
\(\chi_{6069}(40,\cdot)\)	6069.bt	48	no	\(1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{6069}(41,\cdot)\)	6069.cr	272	yes	\(-1\)	\(1\)	\(e\left(\frac{129}{136}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{263}{272}\right)\)	\(e\left(\frac{115}{136}\right)\)	\(e\left(\frac{249}{272}\right)\)	\(e\left(\frac{261}{272}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{235}{272}\right)\)
\(\chi_{6069}(43,\cdot)\)	6069.ck	136	no	\(1\)	\(1\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{37}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{19}{136}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)
\(\chi_{6069}(44,\cdot)\)	6069.cz	816	yes	\(1\)	\(1\)	\(e\left(\frac{275}{408}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(e\left(\frac{373}{816}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{107}{816}\right)\)	\(e\left(\frac{743}{816}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{71}{102}\right)\)	\(e\left(\frac{167}{408}\right)\)	\(e\left(\frac{219}{272}\right)\)
\(\chi_{6069}(46,\cdot)\)	6069.db	816	no	\(-1\)	\(1\)	\(e\left(\frac{337}{408}\right)\)	\(e\left(\frac{133}{204}\right)\)	\(e\left(\frac{35}{816}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{709}{816}\right)\)	\(e\left(\frac{481}{816}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{241}{408}\right)\)	\(e\left(\frac{189}{272}\right)\)
\(\chi_{6069}(47,\cdot)\)	6069.cp	204	yes	\(1\)	\(1\)	\(e\left(\frac{1}{51}\right)\)	\(e\left(\frac{2}{51}\right)\)	\(e\left(\frac{175}{204}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{4}{51}\right)\)	\(e\left(\frac{16}{51}\right)\)	\(e\left(\frac{61}{68}\right)\)
\(\chi_{6069}(50,\cdot)\)	6069.bo	34	no	\(-1\)	\(1\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)
\(\chi_{6069}(52,\cdot)\)	6069.cg	102	no	\(-1\)	\(1\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{19}{51}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{38}{51}\right)\)	\(e\left(\frac{49}{102}\right)\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{6069}(53,\cdot)\)	6069.cw	408	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{204}\right)\)	\(e\left(\frac{47}{102}\right)\)	\(e\left(\frac{109}{408}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{407}{408}\right)\)	\(e\left(\frac{239}{408}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{47}{51}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{99}{136}\right)\)
\(\chi_{6069}(55,\cdot)\)	6069.ca	68	no	\(-1\)	\(1\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)
\(\chi_{6069}(58,\cdot)\)	6069.db	816	no	\(-1\)	\(1\)	\(e\left(\frac{287}{408}\right)\)	\(e\left(\frac{83}{204}\right)\)	\(e\left(\frac{709}{816}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{467}{816}\right)\)	\(e\left(\frac{791}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{359}{408}\right)\)	\(e\left(\frac{75}{272}\right)\)
\(\chi_{6069}(59,\cdot)\)	6069.cv	408	yes	\(1\)	\(1\)	\(e\left(\frac{59}{204}\right)\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{139}{408}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{257}{408}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{8}{51}\right)\)	\(e\left(\frac{179}{204}\right)\)	\(e\left(\frac{125}{136}\right)\)

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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.