LMFDB - Group of Dirichlet characters of modulus 1009

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1009)

pari: g = idealstar(,1009,2)

Character group

sage: G.order() pari: g.no
Order	=	1008
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1008}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1009}(11,\cdot)$

First 32 of 1008 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1009}(1,\cdot)$	1009.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1009}(2,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{193}{252}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{1}{252}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{443}{504}\right)$
$\chi_{1009}(3,\cdot)$	1009.z	168	yes	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{17}{168}\right)$
$\chi_{1009}(4,\cdot)$	1009.ba	252	yes	$1$	$1$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{191}{252}\right)$
$\chi_{1009}(5,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{1}{252}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{205}{252}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{347}{504}\right)$
$\chi_{1009}(6,\cdot)$	1009.ba	252	yes	$1$	$1$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{247}{252}\right)$
$\chi_{1009}(7,\cdot)$	1009.ba	252	yes	$1$	$1$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{197}{252}\right)$
$\chi_{1009}(8,\cdot)$	1009.z	168	yes	$1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{107}{168}\right)$
$\chi_{1009}(9,\cdot)$	1009.v	84	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{84}\right)$
$\chi_{1009}(10,\cdot)$	1009.ba	252	yes	$1$	$1$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{143}{252}\right)$
$\chi_{1009}(11,\cdot)$	1009.bd	1008	yes	$-1$	$1$	$e\left(\frac{443}{504}\right)$	$e\left(\frac{17}{168}\right)$	$e\left(\frac{191}{252}\right)$	$e\left(\frac{347}{504}\right)$	$e\left(\frac{247}{252}\right)$	$e\left(\frac{197}{252}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{143}{252}\right)$	$e\left(\frac{1}{1008}\right)$
$\chi_{1009}(12,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{47}{252}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{59}{252}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{433}{504}\right)$
$\chi_{1009}(13,\cdot)$	1009.r	48	yes	$-1$	$1$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{1009}(14,\cdot)$	1009.s	56	yes	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{37}{56}\right)$
$\chi_{1009}(15,\cdot)$	1009.ba	252	yes	$1$	$1$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{199}{252}\right)$
$\chi_{1009}(16,\cdot)$	1009.x	126	yes	$1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{65}{126}\right)$
$\chi_{1009}(17,\cdot)$	1009.bd	1008	yes	$-1$	$1$	$e\left(\frac{347}{504}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{95}{252}\right)$	$e\left(\frac{323}{504}\right)$	$e\left(\frac{235}{252}\right)$	$e\left(\frac{65}{252}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{83}{252}\right)$	$e\left(\frac{457}{1008}\right)$
$\chi_{1009}(18,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{19}{252}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{115}{252}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{41}{504}\right)$
$\chi_{1009}(19,\cdot)$	1009.r	48	yes	$-1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{1009}(20,\cdot)$	1009.s	56	yes	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{56}\right)$
$\chi_{1009}(21,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{71}{252}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{191}{252}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{445}{504}\right)$
$\chi_{1009}(22,\cdot)$	1009.bd	1008	yes	$-1$	$1$	$e\left(\frac{325}{504}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{73}{252}\right)$	$e\left(\frac{349}{504}\right)$	$e\left(\frac{101}{252}\right)$	$e\left(\frac{103}{252}\right)$	$e\left(\frac{157}{168}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{887}{1008}\right)$
$\chi_{1009}(23,\cdot)$	1009.bb	336	yes	$-1$	$1$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{115}{336}\right)$
$\chi_{1009}(24,\cdot)$	1009.q	42	yes	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{1009}(25,\cdot)$	1009.ba	252	yes	$1$	$1$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{95}{252}\right)$
$\chi_{1009}(26,\cdot)$	1009.bd	1008	yes	$-1$	$1$	$e\left(\frac{281}{504}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{29}{252}\right)$	$e\left(\frac{401}{504}\right)$	$e\left(\frac{85}{252}\right)$	$e\left(\frac{179}{252}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{89}{252}\right)$	$e\left(\frac{235}{1008}\right)$
$\chi_{1009}(27,\cdot)$	1009.s	56	yes	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{56}\right)$
$\chi_{1009}(28,\cdot)$	1009.t	63	yes	$1$	$1$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{1009}(29,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{199}{252}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{223}{252}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{257}{504}\right)$
$\chi_{1009}(30,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{107}{252}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{11}{252}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{337}{504}\right)$
$\chi_{1009}(31,\cdot)$	1009.bd	1008	yes	$-1$	$1$	$e\left(\frac{433}{504}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{181}{252}\right)$	$e\left(\frac{313}{504}\right)$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{31}{252}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{121}{252}\right)$	$e\left(\frac{563}{1008}\right)$
$\chi_{1009}(32,\cdot)$	1009.bc	504	yes	$1$	$1$	$e\left(\frac{209}{252}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{5}{252}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{199}{504}\right)$

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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	$1009$
Structure	\(C_{1008}\)
Order	$1008$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1009}(1,\cdot)\)	1009.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1009}(2,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{193}{252}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{1}{252}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{443}{504}\right)\)
\(\chi_{1009}(3,\cdot)\)	1009.z	168	yes	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{17}{168}\right)\)
\(\chi_{1009}(4,\cdot)\)	1009.ba	252	yes	\(1\)	\(1\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{191}{252}\right)\)
\(\chi_{1009}(5,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{1}{252}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{205}{252}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{347}{504}\right)\)
\(\chi_{1009}(6,\cdot)\)	1009.ba	252	yes	\(1\)	\(1\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{247}{252}\right)\)
\(\chi_{1009}(7,\cdot)\)	1009.ba	252	yes	\(1\)	\(1\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{197}{252}\right)\)
\(\chi_{1009}(8,\cdot)\)	1009.z	168	yes	\(1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{107}{168}\right)\)
\(\chi_{1009}(9,\cdot)\)	1009.v	84	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)
\(\chi_{1009}(10,\cdot)\)	1009.ba	252	yes	\(1\)	\(1\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{143}{252}\right)\)
\(\chi_{1009}(11,\cdot)\)	1009.bd	1008	yes	\(-1\)	\(1\)	\(e\left(\frac{443}{504}\right)\)	\(e\left(\frac{17}{168}\right)\)	\(e\left(\frac{191}{252}\right)\)	\(e\left(\frac{347}{504}\right)\)	\(e\left(\frac{247}{252}\right)\)	\(e\left(\frac{197}{252}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{143}{252}\right)\)	\(e\left(\frac{1}{1008}\right)\)
\(\chi_{1009}(12,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{47}{252}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{59}{252}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{433}{504}\right)\)
\(\chi_{1009}(13,\cdot)\)	1009.r	48	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{1009}(14,\cdot)\)	1009.s	56	yes	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)
\(\chi_{1009}(15,\cdot)\)	1009.ba	252	yes	\(1\)	\(1\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{199}{252}\right)\)
\(\chi_{1009}(16,\cdot)\)	1009.x	126	yes	\(1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)
\(\chi_{1009}(17,\cdot)\)	1009.bd	1008	yes	\(-1\)	\(1\)	\(e\left(\frac{347}{504}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{95}{252}\right)\)	\(e\left(\frac{323}{504}\right)\)	\(e\left(\frac{235}{252}\right)\)	\(e\left(\frac{65}{252}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{83}{252}\right)\)	\(e\left(\frac{457}{1008}\right)\)
\(\chi_{1009}(18,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{19}{252}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{115}{252}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{41}{504}\right)\)
\(\chi_{1009}(19,\cdot)\)	1009.r	48	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{1009}(20,\cdot)\)	1009.s	56	yes	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{56}\right)\)
\(\chi_{1009}(21,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{71}{252}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{191}{252}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{445}{504}\right)\)
\(\chi_{1009}(22,\cdot)\)	1009.bd	1008	yes	\(-1\)	\(1\)	\(e\left(\frac{325}{504}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{73}{252}\right)\)	\(e\left(\frac{349}{504}\right)\)	\(e\left(\frac{101}{252}\right)\)	\(e\left(\frac{103}{252}\right)\)	\(e\left(\frac{157}{168}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{887}{1008}\right)\)
\(\chi_{1009}(23,\cdot)\)	1009.bb	336	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{115}{336}\right)\)
\(\chi_{1009}(24,\cdot)\)	1009.q	42	yes	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{1009}(25,\cdot)\)	1009.ba	252	yes	\(1\)	\(1\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{95}{252}\right)\)
\(\chi_{1009}(26,\cdot)\)	1009.bd	1008	yes	\(-1\)	\(1\)	\(e\left(\frac{281}{504}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{29}{252}\right)\)	\(e\left(\frac{401}{504}\right)\)	\(e\left(\frac{85}{252}\right)\)	\(e\left(\frac{179}{252}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{89}{252}\right)\)	\(e\left(\frac{235}{1008}\right)\)
\(\chi_{1009}(27,\cdot)\)	1009.s	56	yes	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{56}\right)\)
\(\chi_{1009}(28,\cdot)\)	1009.t	63	yes	\(1\)	\(1\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{1009}(29,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{199}{252}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{223}{252}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{257}{504}\right)\)
\(\chi_{1009}(30,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{107}{252}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{11}{252}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{337}{504}\right)\)
\(\chi_{1009}(31,\cdot)\)	1009.bd	1008	yes	\(-1\)	\(1\)	\(e\left(\frac{433}{504}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{181}{252}\right)\)	\(e\left(\frac{313}{504}\right)\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{31}{252}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{121}{252}\right)\)	\(e\left(\frac{563}{1008}\right)\)
\(\chi_{1009}(32,\cdot)\)	1009.bc	504	yes	\(1\)	\(1\)	\(e\left(\frac{209}{252}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{5}{252}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{199}{504}\right)\)

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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.