LMFDB - Group of Dirichlet characters of modulus 3015

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3015)

pari: g = idealstar(,3015,2)

Character group

sage: G.order() pari: g.no
Order	=	1584
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{132}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3015}(1676,\cdot)$, $\chi_{3015}(1207,\cdot)$, $\chi_{3015}(136,\cdot)$

First 32 of 1584 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	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{3015}(1,\cdot)$	3015.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3015}(2,\cdot)$	3015.ep	132	yes	$-1$	$1$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{3015}(4,\cdot)$	3015.dx	66	yes	$1$	$1$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{3015}(7,\cdot)$	3015.ek	132	yes	$1$	$1$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{3015}(8,\cdot)$	3015.cu	44	no	$-1$	$1$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{3015}(11,\cdot)$	3015.du	66	no	$1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{3015}(13,\cdot)$	3015.ek	132	yes	$1$	$1$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{25}{66}\right)$
$\chi_{3015}(14,\cdot)$	3015.do	66	yes	$-1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{3015}(16,\cdot)$	3015.cq	33	no	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{20}{33}\right)$
$\chi_{3015}(17,\cdot)$	3015.ec	132	no	$1$	$1$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{13}{66}\right)$
$\chi_{3015}(19,\cdot)$	3015.df	66	no	$1$	$1$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{3015}(22,\cdot)$	3015.eh	132	yes	$-1$	$1$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{3015}(23,\cdot)$	3015.el	132	yes	$1$	$1$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{3015}(26,\cdot)$	3015.di	66	no	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{3015}(28,\cdot)$	3015.ef	132	no	$1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{19}{66}\right)$
$\chi_{3015}(29,\cdot)$	3015.u	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{3015}(31,\cdot)$	3015.dw	66	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{3015}(32,\cdot)$	3015.ep	132	yes	$-1$	$1$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{113}{132}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{17}{66}\right)$
$\chi_{3015}(34,\cdot)$	3015.dn	66	yes	$-1$	$1$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{28}{33}\right)$
$\chi_{3015}(37,\cdot)$	3015.bz	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{3015}(38,\cdot)$	3015.ch	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$i$	$1$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{3015}(41,\cdot)$	3015.cz	66	no	$1$	$1$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{1}{33}\right)$
$\chi_{3015}(43,\cdot)$	3015.ed	132	yes	$1$	$1$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{3015}(44,\cdot)$	3015.dk	66	no	$1$	$1$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{8}{33}\right)$
$\chi_{3015}(46,\cdot)$	3015.dd	66	no	$-1$	$1$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{3015}(47,\cdot)$	3015.el	132	yes	$1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{3015}(49,\cdot)$	3015.dl	66	yes	$1$	$1$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{3015}(52,\cdot)$	3015.ed	132	yes	$1$	$1$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{3015}(53,\cdot)$	3015.cu	44	no	$-1$	$1$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{3015}(56,\cdot)$	3015.dc	66	no	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{31}{33}\right)$
$\chi_{3015}(58,\cdot)$	3015.ed	132	yes	$1$	$1$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{3015}(59,\cdot)$	3015.do	66	yes	$-1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{11}\right)$

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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	$3015$
Structure	\(C_{2}\times C_{6}\times C_{132}\)
Order	$1584$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(7\)	\(8\)	\(11\)	\(13\)	\(14\)	\(16\)	\(17\)	\(19\)
\(\chi_{3015}(1,\cdot)\)	3015.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3015}(2,\cdot)\)	3015.ep	132	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{3015}(4,\cdot)\)	3015.dx	66	yes	\(1\)	\(1\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{3015}(7,\cdot)\)	3015.ek	132	yes	\(1\)	\(1\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{3015}(8,\cdot)\)	3015.cu	44	no	\(-1\)	\(1\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{3015}(11,\cdot)\)	3015.du	66	no	\(1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{3015}(13,\cdot)\)	3015.ek	132	yes	\(1\)	\(1\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)
\(\chi_{3015}(14,\cdot)\)	3015.do	66	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{3015}(16,\cdot)\)	3015.cq	33	no	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)
\(\chi_{3015}(17,\cdot)\)	3015.ec	132	no	\(1\)	\(1\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{13}{66}\right)\)
\(\chi_{3015}(19,\cdot)\)	3015.df	66	no	\(1\)	\(1\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{3015}(22,\cdot)\)	3015.eh	132	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{3015}(23,\cdot)\)	3015.el	132	yes	\(1\)	\(1\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{3015}(26,\cdot)\)	3015.di	66	no	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{3015}(28,\cdot)\)	3015.ef	132	no	\(1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{19}{66}\right)\)
\(\chi_{3015}(29,\cdot)\)	3015.u	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{3015}(31,\cdot)\)	3015.dw	66	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{3015}(32,\cdot)\)	3015.ep	132	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{113}{132}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)
\(\chi_{3015}(34,\cdot)\)	3015.dn	66	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)
\(\chi_{3015}(37,\cdot)\)	3015.bz	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{3015}(38,\cdot)\)	3015.ch	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{3015}(41,\cdot)\)	3015.cz	66	no	\(1\)	\(1\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)
\(\chi_{3015}(43,\cdot)\)	3015.ed	132	yes	\(1\)	\(1\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{3015}(44,\cdot)\)	3015.dk	66	no	\(1\)	\(1\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)
\(\chi_{3015}(46,\cdot)\)	3015.dd	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{3015}(47,\cdot)\)	3015.el	132	yes	\(1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{3015}(49,\cdot)\)	3015.dl	66	yes	\(1\)	\(1\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{3015}(52,\cdot)\)	3015.ed	132	yes	\(1\)	\(1\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{3015}(53,\cdot)\)	3015.cu	44	no	\(-1\)	\(1\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{3015}(56,\cdot)\)	3015.dc	66	no	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{31}{33}\right)\)
\(\chi_{3015}(58,\cdot)\)	3015.ed	132	yes	\(1\)	\(1\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{3015}(59,\cdot)\)	3015.do	66	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)

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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.