LMFDB - Group of Dirichlet characters of modulus 4009

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4009)

pari: g = idealstar(,4009,2)

Character group

sage: G.order() pari: g.no
Order	=	3780
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{630}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4009}(2111,\cdot)$, $\chi_{4009}(1901,\cdot)$

First 32 of 3780 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4009}(1,\cdot)$	4009.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4009}(2,\cdot)$	4009.et	630	yes	$1$	$1$	$e\left(\frac{19}{315}\right)$	$e\left(\frac{292}{315}\right)$	$e\left(\frac{38}{315}\right)$	$e\left(\frac{163}{315}\right)$	$e\left(\frac{311}{315}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{269}{315}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{46}{105}\right)$
$\chi_{4009}(3,\cdot)$	4009.et	630	yes	$1$	$1$	$e\left(\frac{292}{315}\right)$	$e\left(\frac{61}{315}\right)$	$e\left(\frac{269}{315}\right)$	$e\left(\frac{184}{315}\right)$	$e\left(\frac{38}{315}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{122}{315}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{88}{105}\right)$
$\chi_{4009}(4,\cdot)$	4009.em	315	yes	$1$	$1$	$e\left(\frac{38}{315}\right)$	$e\left(\frac{269}{315}\right)$	$e\left(\frac{76}{315}\right)$	$e\left(\frac{11}{315}\right)$	$e\left(\frac{307}{315}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{223}{315}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{92}{105}\right)$
$\chi_{4009}(5,\cdot)$	4009.en	315	yes	$1$	$1$	$e\left(\frac{163}{315}\right)$	$e\left(\frac{184}{315}\right)$	$e\left(\frac{11}{315}\right)$	$e\left(\frac{61}{315}\right)$	$e\left(\frac{32}{315}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{53}{315}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{52}{105}\right)$
$\chi_{4009}(6,\cdot)$	4009.em	315	yes	$1$	$1$	$e\left(\frac{311}{315}\right)$	$e\left(\frac{38}{315}\right)$	$e\left(\frac{307}{315}\right)$	$e\left(\frac{32}{315}\right)$	$e\left(\frac{34}{315}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{76}{315}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{29}{105}\right)$
$\chi_{4009}(7,\cdot)$	4009.eh	210	yes	$-1$	$1$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{167}{210}\right)$	$e\left(\frac{104}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{83}{105}\right)$	$e\left(\frac{1}{210}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{35}\right)$
$\chi_{4009}(8,\cdot)$	4009.ec	210	yes	$1$	$1$	$e\left(\frac{19}{105}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{58}{105}\right)$	$e\left(\frac{101}{105}\right)$	$e\left(\frac{69}{70}\right)$	$e\left(\frac{19}{35}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{35}\right)$
$\chi_{4009}(9,\cdot)$	4009.em	315	yes	$1$	$1$	$e\left(\frac{269}{315}\right)$	$e\left(\frac{122}{315}\right)$	$e\left(\frac{223}{315}\right)$	$e\left(\frac{53}{315}\right)$	$e\left(\frac{76}{315}\right)$	$e\left(\frac{62}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{244}{315}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{71}{105}\right)$
$\chi_{4009}(10,\cdot)$	4009.dm	90	yes	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{4009}(11,\cdot)$	4009.do	105	yes	$1$	$1$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{88}{105}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{71}{105}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{34}{35}\right)$
$\chi_{4009}(12,\cdot)$	4009.cs	42	yes	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{4009}(13,\cdot)$	4009.es	630	yes	$-1$	$1$	$e\left(\frac{607}{630}\right)$	$e\left(\frac{61}{630}\right)$	$e\left(\frac{292}{315}\right)$	$e\left(\frac{302}{315}\right)$	$e\left(\frac{19}{315}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{187}{210}\right)$	$e\left(\frac{61}{315}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{4009}(14,\cdot)$	4009.br	18	yes	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{4009}(15,\cdot)$	4009.bj	18	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{4009}(16,\cdot)$	4009.em	315	yes	$1$	$1$	$e\left(\frac{76}{315}\right)$	$e\left(\frac{223}{315}\right)$	$e\left(\frac{152}{315}\right)$	$e\left(\frac{22}{315}\right)$	$e\left(\frac{299}{315}\right)$	$e\left(\frac{103}{105}\right)$	$e\left(\frac{76}{105}\right)$	$e\left(\frac{131}{315}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{79}{105}\right)$
$\chi_{4009}(17,\cdot)$	4009.ev	630	yes	$-1$	$1$	$e\left(\frac{317}{630}\right)$	$e\left(\frac{611}{630}\right)$	$e\left(\frac{2}{315}\right)$	$e\left(\frac{307}{315}\right)$	$e\left(\frac{149}{315}\right)$	$e\left(\frac{11}{210}\right)$	$e\left(\frac{107}{210}\right)$	$e\left(\frac{296}{315}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{19}{105}\right)$
$\chi_{4009}(18,\cdot)$	4009.dd	70	yes	$1$	$1$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{11}{35}\right)$	$e\left(\frac{29}{35}\right)$	$e\left(\frac{24}{35}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{41}{70}\right)$	$e\left(\frac{26}{35}\right)$	$e\left(\frac{22}{35}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{35}\right)$
$\chi_{4009}(20,\cdot)$	4009.dp	105	no	$1$	$1$	$e\left(\frac{67}{105}\right)$	$e\left(\frac{46}{105}\right)$	$e\left(\frac{29}{105}\right)$	$e\left(\frac{8}{35}\right)$	$e\left(\frac{8}{105}\right)$	$e\left(\frac{73}{105}\right)$	$e\left(\frac{32}{35}\right)$	$e\left(\frac{92}{105}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{35}\right)$
$\chi_{4009}(21,\cdot)$	4009.de	90	yes	$-1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{4009}(22,\cdot)$	4009.et	630	yes	$1$	$1$	$e\left(\frac{157}{315}\right)$	$e\left(\frac{241}{315}\right)$	$e\left(\frac{314}{315}\right)$	$e\left(\frac{4}{315}\right)$	$e\left(\frac{83}{315}\right)$	$e\left(\frac{47}{210}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{167}{315}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{43}{105}\right)$
$\chi_{4009}(23,\cdot)$	4009.df	90	yes	$-1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{4009}(24,\cdot)$	4009.em	315	yes	$1$	$1$	$e\left(\frac{34}{315}\right)$	$e\left(\frac{307}{315}\right)$	$e\left(\frac{68}{315}\right)$	$e\left(\frac{43}{315}\right)$	$e\left(\frac{26}{315}\right)$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{34}{105}\right)$	$e\left(\frac{299}{315}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{16}{105}\right)$
$\chi_{4009}(25,\cdot)$	4009.en	315	yes	$1$	$1$	$e\left(\frac{11}{315}\right)$	$e\left(\frac{53}{315}\right)$	$e\left(\frac{22}{315}\right)$	$e\left(\frac{122}{315}\right)$	$e\left(\frac{64}{315}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{11}{105}\right)$	$e\left(\frac{106}{315}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{104}{105}\right)$
$\chi_{4009}(26,\cdot)$	4009.cn	42	yes	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{21}\right)$	$-1$	$e\left(\frac{6}{7}\right)$
$\chi_{4009}(27,\cdot)$	4009.ec	210	yes	$1$	$1$	$e\left(\frac{82}{105}\right)$	$e\left(\frac{61}{105}\right)$	$e\left(\frac{59}{105}\right)$	$e\left(\frac{79}{105}\right)$	$e\left(\frac{38}{105}\right)$	$e\left(\frac{27}{70}\right)$	$e\left(\frac{12}{35}\right)$	$e\left(\frac{17}{105}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{18}{35}\right)$
$\chi_{4009}(28,\cdot)$	4009.ew	630	yes	$-1$	$1$	$e\left(\frac{73}{630}\right)$	$e\left(\frac{409}{630}\right)$	$e\left(\frac{73}{315}\right)$	$e\left(\frac{233}{315}\right)$	$e\left(\frac{241}{315}\right)$	$e\left(\frac{209}{210}\right)$	$e\left(\frac{73}{210}\right)$	$e\left(\frac{94}{315}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{11}{105}\right)$
$\chi_{4009}(29,\cdot)$	4009.et	630	yes	$1$	$1$	$e\left(\frac{251}{315}\right)$	$e\left(\frac{293}{315}\right)$	$e\left(\frac{187}{315}\right)$	$e\left(\frac{197}{315}\right)$	$e\left(\frac{229}{315}\right)$	$e\left(\frac{31}{210}\right)$	$e\left(\frac{41}{105}\right)$	$e\left(\frac{271}{315}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{44}{105}\right)$
$\chi_{4009}(30,\cdot)$	4009.dn	105	yes	$1$	$1$	$e\left(\frac{53}{105}\right)$	$e\left(\frac{74}{105}\right)$	$e\left(\frac{1}{105}\right)$	$e\left(\frac{31}{105}\right)$	$e\left(\frac{22}{105}\right)$	$e\left(\frac{52}{105}\right)$	$e\left(\frac{18}{35}\right)$	$e\left(\frac{43}{105}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{35}\right)$
$\chi_{4009}(31,\cdot)$	4009.cr	42	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{16}{21}\right)$	$1$	$e\left(\frac{5}{7}\right)$
$\chi_{4009}(32,\cdot)$	4009.dv	126	yes	$1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{4009}(33,\cdot)$	4009.dv	126	yes	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{21}\right)$

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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	$4009$
Structure	\(C_{6}\times C_{630}\)
Order	$3780$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4009}(1,\cdot)\)	4009.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4009}(2,\cdot)\)	4009.et	630	yes	\(1\)	\(1\)	\(e\left(\frac{19}{315}\right)\)	\(e\left(\frac{292}{315}\right)\)	\(e\left(\frac{38}{315}\right)\)	\(e\left(\frac{163}{315}\right)\)	\(e\left(\frac{311}{315}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{269}{315}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{46}{105}\right)\)
\(\chi_{4009}(3,\cdot)\)	4009.et	630	yes	\(1\)	\(1\)	\(e\left(\frac{292}{315}\right)\)	\(e\left(\frac{61}{315}\right)\)	\(e\left(\frac{269}{315}\right)\)	\(e\left(\frac{184}{315}\right)\)	\(e\left(\frac{38}{315}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{122}{315}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{88}{105}\right)\)
\(\chi_{4009}(4,\cdot)\)	4009.em	315	yes	\(1\)	\(1\)	\(e\left(\frac{38}{315}\right)\)	\(e\left(\frac{269}{315}\right)\)	\(e\left(\frac{76}{315}\right)\)	\(e\left(\frac{11}{315}\right)\)	\(e\left(\frac{307}{315}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{223}{315}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{92}{105}\right)\)
\(\chi_{4009}(5,\cdot)\)	4009.en	315	yes	\(1\)	\(1\)	\(e\left(\frac{163}{315}\right)\)	\(e\left(\frac{184}{315}\right)\)	\(e\left(\frac{11}{315}\right)\)	\(e\left(\frac{61}{315}\right)\)	\(e\left(\frac{32}{315}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{53}{315}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{52}{105}\right)\)
\(\chi_{4009}(6,\cdot)\)	4009.em	315	yes	\(1\)	\(1\)	\(e\left(\frac{311}{315}\right)\)	\(e\left(\frac{38}{315}\right)\)	\(e\left(\frac{307}{315}\right)\)	\(e\left(\frac{32}{315}\right)\)	\(e\left(\frac{34}{315}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{76}{315}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{29}{105}\right)\)
\(\chi_{4009}(7,\cdot)\)	4009.eh	210	yes	\(-1\)	\(1\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{167}{210}\right)\)	\(e\left(\frac{104}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{83}{105}\right)\)	\(e\left(\frac{1}{210}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{35}\right)\)
\(\chi_{4009}(8,\cdot)\)	4009.ec	210	yes	\(1\)	\(1\)	\(e\left(\frac{19}{105}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{58}{105}\right)\)	\(e\left(\frac{101}{105}\right)\)	\(e\left(\frac{69}{70}\right)\)	\(e\left(\frac{19}{35}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{35}\right)\)
\(\chi_{4009}(9,\cdot)\)	4009.em	315	yes	\(1\)	\(1\)	\(e\left(\frac{269}{315}\right)\)	\(e\left(\frac{122}{315}\right)\)	\(e\left(\frac{223}{315}\right)\)	\(e\left(\frac{53}{315}\right)\)	\(e\left(\frac{76}{315}\right)\)	\(e\left(\frac{62}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{244}{315}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{71}{105}\right)\)
\(\chi_{4009}(10,\cdot)\)	4009.dm	90	yes	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{4009}(11,\cdot)\)	4009.do	105	yes	\(1\)	\(1\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{88}{105}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{71}{105}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{34}{35}\right)\)
\(\chi_{4009}(12,\cdot)\)	4009.cs	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4009}(13,\cdot)\)	4009.es	630	yes	\(-1\)	\(1\)	\(e\left(\frac{607}{630}\right)\)	\(e\left(\frac{61}{630}\right)\)	\(e\left(\frac{292}{315}\right)\)	\(e\left(\frac{302}{315}\right)\)	\(e\left(\frac{19}{315}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{187}{210}\right)\)	\(e\left(\frac{61}{315}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{4009}(14,\cdot)\)	4009.br	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{4009}(15,\cdot)\)	4009.bj	18	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{4009}(16,\cdot)\)	4009.em	315	yes	\(1\)	\(1\)	\(e\left(\frac{76}{315}\right)\)	\(e\left(\frac{223}{315}\right)\)	\(e\left(\frac{152}{315}\right)\)	\(e\left(\frac{22}{315}\right)\)	\(e\left(\frac{299}{315}\right)\)	\(e\left(\frac{103}{105}\right)\)	\(e\left(\frac{76}{105}\right)\)	\(e\left(\frac{131}{315}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{79}{105}\right)\)
\(\chi_{4009}(17,\cdot)\)	4009.ev	630	yes	\(-1\)	\(1\)	\(e\left(\frac{317}{630}\right)\)	\(e\left(\frac{611}{630}\right)\)	\(e\left(\frac{2}{315}\right)\)	\(e\left(\frac{307}{315}\right)\)	\(e\left(\frac{149}{315}\right)\)	\(e\left(\frac{11}{210}\right)\)	\(e\left(\frac{107}{210}\right)\)	\(e\left(\frac{296}{315}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{19}{105}\right)\)
\(\chi_{4009}(18,\cdot)\)	4009.dd	70	yes	\(1\)	\(1\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{11}{35}\right)\)	\(e\left(\frac{29}{35}\right)\)	\(e\left(\frac{24}{35}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{41}{70}\right)\)	\(e\left(\frac{26}{35}\right)\)	\(e\left(\frac{22}{35}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{35}\right)\)
\(\chi_{4009}(20,\cdot)\)	4009.dp	105	no	\(1\)	\(1\)	\(e\left(\frac{67}{105}\right)\)	\(e\left(\frac{46}{105}\right)\)	\(e\left(\frac{29}{105}\right)\)	\(e\left(\frac{8}{35}\right)\)	\(e\left(\frac{8}{105}\right)\)	\(e\left(\frac{73}{105}\right)\)	\(e\left(\frac{32}{35}\right)\)	\(e\left(\frac{92}{105}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{35}\right)\)
\(\chi_{4009}(21,\cdot)\)	4009.de	90	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{4009}(22,\cdot)\)	4009.et	630	yes	\(1\)	\(1\)	\(e\left(\frac{157}{315}\right)\)	\(e\left(\frac{241}{315}\right)\)	\(e\left(\frac{314}{315}\right)\)	\(e\left(\frac{4}{315}\right)\)	\(e\left(\frac{83}{315}\right)\)	\(e\left(\frac{47}{210}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{167}{315}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{43}{105}\right)\)
\(\chi_{4009}(23,\cdot)\)	4009.df	90	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{4009}(24,\cdot)\)	4009.em	315	yes	\(1\)	\(1\)	\(e\left(\frac{34}{315}\right)\)	\(e\left(\frac{307}{315}\right)\)	\(e\left(\frac{68}{315}\right)\)	\(e\left(\frac{43}{315}\right)\)	\(e\left(\frac{26}{315}\right)\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{34}{105}\right)\)	\(e\left(\frac{299}{315}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{16}{105}\right)\)
\(\chi_{4009}(25,\cdot)\)	4009.en	315	yes	\(1\)	\(1\)	\(e\left(\frac{11}{315}\right)\)	\(e\left(\frac{53}{315}\right)\)	\(e\left(\frac{22}{315}\right)\)	\(e\left(\frac{122}{315}\right)\)	\(e\left(\frac{64}{315}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{11}{105}\right)\)	\(e\left(\frac{106}{315}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{104}{105}\right)\)
\(\chi_{4009}(26,\cdot)\)	4009.cn	42	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{4009}(27,\cdot)\)	4009.ec	210	yes	\(1\)	\(1\)	\(e\left(\frac{82}{105}\right)\)	\(e\left(\frac{61}{105}\right)\)	\(e\left(\frac{59}{105}\right)\)	\(e\left(\frac{79}{105}\right)\)	\(e\left(\frac{38}{105}\right)\)	\(e\left(\frac{27}{70}\right)\)	\(e\left(\frac{12}{35}\right)\)	\(e\left(\frac{17}{105}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{18}{35}\right)\)
\(\chi_{4009}(28,\cdot)\)	4009.ew	630	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{630}\right)\)	\(e\left(\frac{409}{630}\right)\)	\(e\left(\frac{73}{315}\right)\)	\(e\left(\frac{233}{315}\right)\)	\(e\left(\frac{241}{315}\right)\)	\(e\left(\frac{209}{210}\right)\)	\(e\left(\frac{73}{210}\right)\)	\(e\left(\frac{94}{315}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{11}{105}\right)\)
\(\chi_{4009}(29,\cdot)\)	4009.et	630	yes	\(1\)	\(1\)	\(e\left(\frac{251}{315}\right)\)	\(e\left(\frac{293}{315}\right)\)	\(e\left(\frac{187}{315}\right)\)	\(e\left(\frac{197}{315}\right)\)	\(e\left(\frac{229}{315}\right)\)	\(e\left(\frac{31}{210}\right)\)	\(e\left(\frac{41}{105}\right)\)	\(e\left(\frac{271}{315}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{44}{105}\right)\)
\(\chi_{4009}(30,\cdot)\)	4009.dn	105	yes	\(1\)	\(1\)	\(e\left(\frac{53}{105}\right)\)	\(e\left(\frac{74}{105}\right)\)	\(e\left(\frac{1}{105}\right)\)	\(e\left(\frac{31}{105}\right)\)	\(e\left(\frac{22}{105}\right)\)	\(e\left(\frac{52}{105}\right)\)	\(e\left(\frac{18}{35}\right)\)	\(e\left(\frac{43}{105}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{35}\right)\)
\(\chi_{4009}(31,\cdot)\)	4009.cr	42	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{4009}(32,\cdot)\)	4009.dv	126	yes	\(1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{4009}(33,\cdot)\)	4009.dv	126	yes	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{21}\right)\)

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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.