LMFDB - Group of Dirichlet characters of modulus 6040

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6040)

pari: g = idealstar(,6040,2)

Character group

sage: G.order() pari: g.no
Order	=	2400
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{300}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6040}(1511,\cdot)$, $\chi_{6040}(3021,\cdot)$, $\chi_{6040}(2417,\cdot)$, $\chi_{6040}(761,\cdot)$

First 32 of 2400 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{6040}(1,\cdot)$	6040.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6040}(3,\cdot)$	6040.en	100	yes	$-1$	$1$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{97}{100}\right)$
$\chi_{6040}(7,\cdot)$	6040.fi	300	no	$-1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{29}{100}\right)$
$\chi_{6040}(9,\cdot)$	6040.dp	50	no	$1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{6040}(11,\cdot)$	6040.es	150	no	$-1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{73}{150}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{68}{75}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{6040}(13,\cdot)$	6040.fh	300	yes	$1$	$1$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{19}{300}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{29}{150}\right)$	$e\left(\frac{287}{300}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{67}{100}\right)$
$\chi_{6040}(17,\cdot)$	6040.fn	300	no	$-1$	$1$	$e\left(\frac{7}{100}\right)$	$e\left(\frac{47}{300}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{26}{75}\right)$	$e\left(\frac{181}{300}\right)$	$e\left(\frac{203}{300}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{21}{100}\right)$
$\chi_{6040}(19,\cdot)$	6040.bx	10	yes	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$
$\chi_{6040}(21,\cdot)$	6040.fc	150	no	$1$	$1$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{37}{150}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{17}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{6040}(23,\cdot)$	6040.ed	60	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{60}\right)$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{6040}(27,\cdot)$	6040.en	100	yes	$-1$	$1$	$e\left(\frac{97}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{7}{25}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{91}{100}\right)$
$\chi_{6040}(29,\cdot)$	6040.dx	50	yes	$1$	$1$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{25}\right)$
$\chi_{6040}(31,\cdot)$	6040.ez	150	no	$-1$	$1$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{62}{75}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{47}{75}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{50}\right)$
$\chi_{6040}(33,\cdot)$	6040.ce	12	no	$1$	$1$	$-i$	$e\left(\frac{11}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$i$
$\chi_{6040}(37,\cdot)$	6040.fj	300	yes	$-1$	$1$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{119}{300}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{79}{150}\right)$	$e\left(\frac{187}{300}\right)$	$e\left(\frac{131}{300}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{67}{100}\right)$
$\chi_{6040}(39,\cdot)$	6040.ff	150	no	$-1$	$1$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{143}{150}\right)$	$e\left(\frac{127}{150}\right)$	$e\left(\frac{101}{150}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{28}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{16}{25}\right)$
$\chi_{6040}(41,\cdot)$	6040.do	50	no	$-1$	$1$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{6040}(43,\cdot)$	6040.fk	300	yes	$1$	$1$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{247}{300}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{281}{300}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{71}{100}\right)$
$\chi_{6040}(47,\cdot)$	6040.fg	300	no	$1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{109}{300}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{119}{150}\right)$	$e\left(\frac{257}{300}\right)$	$e\left(\frac{91}{300}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{49}{75}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{87}{100}\right)$
$\chi_{6040}(49,\cdot)$	6040.et	150	no	$1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{73}{75}\right)$	$e\left(\frac{19}{150}\right)$	$e\left(\frac{47}{150}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{16}{75}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{6040}(51,\cdot)$	6040.ew	150	no	$1$	$1$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{44}{75}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{8}{75}\right)$	$e\left(\frac{37}{75}\right)$	$e\left(\frac{56}{75}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{50}\right)$
$\chi_{6040}(53,\cdot)$	6040.em	100	yes	$1$	$1$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{100}\right)$
$\chi_{6040}(57,\cdot)$	6040.eq	100	no	$1$	$1$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{100}\right)$
$\chi_{6040}(59,\cdot)$	6040.bx	10	yes	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$
$\chi_{6040}(61,\cdot)$	6040.fb	150	no	$-1$	$1$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{11}{150}\right)$	$e\left(\frac{2}{75}\right)$	$e\left(\frac{1}{75}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{137}{150}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{25}\right)$
$\chi_{6040}(63,\cdot)$	6040.fi	300	no	$-1$	$1$	$e\left(\frac{41}{100}\right)$	$e\left(\frac{161}{300}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{1}{150}\right)$	$e\left(\frac{253}{300}\right)$	$e\left(\frac{89}{300}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{71}{75}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{100}\right)$
$\chi_{6040}(67,\cdot)$	6040.en	100	yes	$-1$	$1$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{89}{100}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{100}\right)$
$\chi_{6040}(69,\cdot)$	6040.fa	150	yes	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{150}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{49}{150}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{43}{150}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{133}{150}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{25}\right)$
$\chi_{6040}(71,\cdot)$	6040.fe	150	no	$1$	$1$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{7}{75}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{23}{150}\right)$	$e\left(\frac{97}{150}\right)$	$e\left(\frac{43}{75}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{58}{75}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{25}\right)$
$\chi_{6040}(73,\cdot)$	6040.eq	100	no	$1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{100}\right)$
$\chi_{6040}(77,\cdot)$	6040.fh	300	yes	$1$	$1$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{49}{300}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{59}{150}\right)$	$e\left(\frac{77}{300}\right)$	$e\left(\frac{151}{300}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{150}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{57}{100}\right)$
$\chi_{6040}(79,\cdot)$	6040.dz	50	no	$1$	$1$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{50}\right)$

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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	$6040$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{300}\)
Order	$2400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{6040}(1,\cdot)\)	6040.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6040}(3,\cdot)\)	6040.en	100	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{97}{100}\right)\)
\(\chi_{6040}(7,\cdot)\)	6040.fi	300	no	\(-1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{29}{100}\right)\)
\(\chi_{6040}(9,\cdot)\)	6040.dp	50	no	\(1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{6040}(11,\cdot)\)	6040.es	150	no	\(-1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{73}{150}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{68}{75}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{25}\right)\)
\(\chi_{6040}(13,\cdot)\)	6040.fh	300	yes	\(1\)	\(1\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{19}{300}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{29}{150}\right)\)	\(e\left(\frac{287}{300}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{67}{100}\right)\)
\(\chi_{6040}(17,\cdot)\)	6040.fn	300	no	\(-1\)	\(1\)	\(e\left(\frac{7}{100}\right)\)	\(e\left(\frac{47}{300}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{26}{75}\right)\)	\(e\left(\frac{181}{300}\right)\)	\(e\left(\frac{203}{300}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{21}{100}\right)\)
\(\chi_{6040}(19,\cdot)\)	6040.bx	10	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{6040}(21,\cdot)\)	6040.fc	150	no	\(1\)	\(1\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{37}{150}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{17}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{6040}(23,\cdot)\)	6040.ed	60	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{6040}(27,\cdot)\)	6040.en	100	yes	\(-1\)	\(1\)	\(e\left(\frac{97}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{7}{25}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{91}{100}\right)\)
\(\chi_{6040}(29,\cdot)\)	6040.dx	50	yes	\(1\)	\(1\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{25}\right)\)
\(\chi_{6040}(31,\cdot)\)	6040.ez	150	no	\(-1\)	\(1\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{62}{75}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{47}{75}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{43}{50}\right)\)
\(\chi_{6040}(33,\cdot)\)	6040.ce	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)
\(\chi_{6040}(37,\cdot)\)	6040.fj	300	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{119}{300}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{79}{150}\right)\)	\(e\left(\frac{187}{300}\right)\)	\(e\left(\frac{131}{300}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{67}{100}\right)\)
\(\chi_{6040}(39,\cdot)\)	6040.ff	150	no	\(-1\)	\(1\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{143}{150}\right)\)	\(e\left(\frac{127}{150}\right)\)	\(e\left(\frac{101}{150}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{28}{75}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{16}{25}\right)\)
\(\chi_{6040}(41,\cdot)\)	6040.do	50	no	\(-1\)	\(1\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{6040}(43,\cdot)\)	6040.fk	300	yes	\(1\)	\(1\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{247}{300}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{281}{300}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{71}{100}\right)\)
\(\chi_{6040}(47,\cdot)\)	6040.fg	300	no	\(1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{109}{300}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{119}{150}\right)\)	\(e\left(\frac{257}{300}\right)\)	\(e\left(\frac{91}{300}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{49}{75}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{87}{100}\right)\)
\(\chi_{6040}(49,\cdot)\)	6040.et	150	no	\(1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{73}{75}\right)\)	\(e\left(\frac{19}{150}\right)\)	\(e\left(\frac{47}{150}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{16}{75}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{6040}(51,\cdot)\)	6040.ew	150	no	\(1\)	\(1\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{44}{75}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{8}{75}\right)\)	\(e\left(\frac{37}{75}\right)\)	\(e\left(\frac{56}{75}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{50}\right)\)
\(\chi_{6040}(53,\cdot)\)	6040.em	100	yes	\(1\)	\(1\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{100}\right)\)
\(\chi_{6040}(57,\cdot)\)	6040.eq	100	no	\(1\)	\(1\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{100}\right)\)
\(\chi_{6040}(59,\cdot)\)	6040.bx	10	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{6040}(61,\cdot)\)	6040.fb	150	no	\(-1\)	\(1\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{11}{150}\right)\)	\(e\left(\frac{2}{75}\right)\)	\(e\left(\frac{1}{75}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{137}{150}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{25}\right)\)
\(\chi_{6040}(63,\cdot)\)	6040.fi	300	no	\(-1\)	\(1\)	\(e\left(\frac{41}{100}\right)\)	\(e\left(\frac{161}{300}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{1}{150}\right)\)	\(e\left(\frac{253}{300}\right)\)	\(e\left(\frac{89}{300}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{71}{75}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{100}\right)\)
\(\chi_{6040}(67,\cdot)\)	6040.en	100	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{89}{100}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{100}\right)\)
\(\chi_{6040}(69,\cdot)\)	6040.fa	150	yes	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{150}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{49}{150}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{43}{150}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{133}{150}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{25}\right)\)
\(\chi_{6040}(71,\cdot)\)	6040.fe	150	no	\(1\)	\(1\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{7}{75}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{23}{150}\right)\)	\(e\left(\frac{97}{150}\right)\)	\(e\left(\frac{43}{75}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{58}{75}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{25}\right)\)
\(\chi_{6040}(73,\cdot)\)	6040.eq	100	no	\(1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{100}\right)\)
\(\chi_{6040}(77,\cdot)\)	6040.fh	300	yes	\(1\)	\(1\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{49}{300}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{59}{150}\right)\)	\(e\left(\frac{77}{300}\right)\)	\(e\left(\frac{151}{300}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{150}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{57}{100}\right)\)
\(\chi_{6040}(79,\cdot)\)	6040.dz	50	no	\(1\)	\(1\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{50}\right)\)

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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.