LMFDB - Group of Dirichlet characters of modulus 10003

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10003)

pari: g = idealstar(,10003,2)

Character group

sage: G.order() pari: g.no
Order	=	8568
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{1428}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10003}(2859,\cdot)$, $\chi_{10003}(2864,\cdot)$

First 32 of 8568 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{10003}(1,\cdot)$	10003.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10003}(2,\cdot)$	10003.cr	84	yes	$-1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{10003}(3,\cdot)$	10003.eh	714	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{655}{714}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{457}{714}\right)$	$e\left(\frac{47}{357}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{298}{357}\right)$	$e\left(\frac{305}{357}\right)$	$e\left(\frac{271}{714}\right)$	$e\left(\frac{247}{714}\right)$
$\chi_{10003}(4,\cdot)$	10003.bt	42	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{10003}(5,\cdot)$	10003.ef	714	yes	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{457}{714}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{365}{714}\right)$	$e\left(\frac{39}{238}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{100}{357}\right)$	$e\left(\frac{25}{714}\right)$	$e\left(\frac{206}{357}\right)$	$e\left(\frac{491}{714}\right)$
$\chi_{10003}(6,\cdot)$	10003.ej	1428	yes	$1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{47}{357}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{39}{238}\right)$	$e\left(\frac{715}{1428}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{94}{357}\right)$	$e\left(\frac{761}{1428}\right)$	$e\left(\frac{1103}{1428}\right)$	$e\left(\frac{207}{238}\right)$
$\chi_{10003}(8,\cdot)$	10003.bo	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{10003}(9,\cdot)$	10003.dq	357	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{298}{357}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{100}{357}\right)$	$e\left(\frac{94}{357}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{239}{357}\right)$	$e\left(\frac{253}{357}\right)$	$e\left(\frac{271}{357}\right)$	$e\left(\frac{247}{357}\right)$
$\chi_{10003}(10,\cdot)$	10003.el	1428	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{305}{357}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{714}\right)$	$e\left(\frac{761}{1428}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{253}{357}\right)$	$e\left(\frac{1019}{1428}\right)$	$e\left(\frac{1385}{1428}\right)$	$e\left(\frac{151}{714}\right)$
$\chi_{10003}(11,\cdot)$	10003.eo	1428	yes	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{271}{714}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{206}{357}\right)$	$e\left(\frac{1103}{1428}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{271}{357}\right)$	$e\left(\frac{1385}{1428}\right)$	$e\left(\frac{905}{1428}\right)$	$e\left(\frac{59}{357}\right)$
$\chi_{10003}(12,\cdot)$	10003.ef	714	yes	$-1$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{247}{714}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{491}{714}\right)$	$e\left(\frac{207}{238}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{247}{357}\right)$	$e\left(\frac{151}{714}\right)$	$e\left(\frac{59}{357}\right)$	$e\left(\frac{281}{714}\right)$
$\chi_{10003}(13,\cdot)$	10003.ea	714	yes	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{71}{714}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{238}\right)$	$e\left(\frac{248}{357}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{71}{357}\right)$	$e\left(\frac{232}{357}\right)$	$e\left(\frac{521}{714}\right)$	$e\left(\frac{69}{238}\right)$
$\chi_{10003}(15,\cdot)$	10003.dz	714	no	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{199}{357}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{18}{119}\right)$	$e\left(\frac{211}{714}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{41}{357}\right)$	$e\left(\frac{635}{714}\right)$	$e\left(\frac{683}{714}\right)$	$e\left(\frac{4}{119}\right)$
$\chi_{10003}(16,\cdot)$	10003.bk	21	yes	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{10003}(17,\cdot)$	10003.dx	714	yes	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{125}{238}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{625}{714}\right)$	$e\left(\frac{145}{357}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{119}\right)$	$e\left(\frac{90}{119}\right)$	$e\left(\frac{39}{238}\right)$	$e\left(\frac{205}{714}\right)$
$\chi_{10003}(18,\cdot)$	10003.di	204	yes	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{102}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{41}{51}\right)$	$e\left(\frac{43}{68}\right)$	$-i$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{31}{204}\right)$	$e\left(\frac{11}{51}\right)$
$\chi_{10003}(19,\cdot)$	10003.dx	714	yes	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{238}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{275}{714}\right)$	$e\left(\frac{278}{357}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{55}{119}\right)$	$e\left(\frac{111}{119}\right)$	$e\left(\frac{179}{238}\right)$	$e\left(\frac{233}{714}\right)$
$\chi_{10003}(20,\cdot)$	10003.cz	102	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{102}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{46}{51}\right)$	$-1$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{37}{102}\right)$	$e\left(\frac{25}{34}\right)$
$\chi_{10003}(22,\cdot)$	10003.dz	714	no	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{212}{357}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{12}{119}\right)$	$e\left(\frac{101}{714}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{67}{357}\right)$	$e\left(\frac{463}{714}\right)$	$e\left(\frac{19}{714}\right)$	$e\left(\frac{82}{119}\right)$
$\chi_{10003}(23,\cdot)$	10003.eg	714	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{97}{357}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{241}{357}\right)$	$e\left(\frac{653}{714}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{194}{357}\right)$	$e\left(\frac{227}{714}\right)$	$e\left(\frac{71}{714}\right)$	$e\left(\frac{199}{357}\right)$
$\chi_{10003}(24,\cdot)$	10003.el	1428	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{200}{357}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{151}{714}\right)$	$e\left(\frac{341}{1428}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{43}{357}\right)$	$e\left(\frac{1271}{1428}\right)$	$e\left(\frac{797}{1428}\right)$	$e\left(\frac{655}{714}\right)$
$\chi_{10003}(25,\cdot)$	10003.dr	357	yes	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{100}{357}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{8}{357}\right)$	$e\left(\frac{39}{119}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{200}{357}\right)$	$e\left(\frac{25}{357}\right)$	$e\left(\frac{55}{357}\right)$	$e\left(\frac{134}{357}\right)$
$\chi_{10003}(26,\cdot)$	10003.dj	204	yes	$1$	$1$	$-i$	$e\left(\frac{16}{51}\right)$	$-1$	$e\left(\frac{59}{102}\right)$	$e\left(\frac{13}{204}\right)$	$i$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{67}{204}\right)$	$e\left(\frac{25}{204}\right)$	$e\left(\frac{83}{102}\right)$
$\chi_{10003}(27,\cdot)$	10003.do	238	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{179}{238}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{219}{238}\right)$	$e\left(\frac{47}{119}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{60}{119}\right)$	$e\left(\frac{67}{119}\right)$	$e\left(\frac{33}{238}\right)$	$e\left(\frac{9}{238}\right)$
$\chi_{10003}(29,\cdot)$	10003.en	1428	no	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{275}{714}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{83}{119}\right)$	$e\left(\frac{227}{1428}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{275}{357}\right)$	$e\left(\frac{673}{1428}\right)$	$e\left(\frac{481}{1428}\right)$	$e\left(\frac{111}{119}\right)$
$\chi_{10003}(30,\cdot)$	10003.eo	1428	yes	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{551}{714}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{241}{357}\right)$	$e\left(\frac{949}{1428}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{194}{357}\right)$	$e\left(\frac{811}{1428}\right)$	$e\left(\frac{499}{1428}\right)$	$e\left(\frac{199}{357}\right)$
$\chi_{10003}(31,\cdot)$	10003.dj	204	yes	$1$	$1$	$i$	$e\left(\frac{5}{51}\right)$	$-1$	$e\left(\frac{79}{102}\right)$	$e\left(\frac{71}{204}\right)$	$-i$	$e\left(\frac{10}{51}\right)$	$e\left(\frac{5}{204}\right)$	$e\left(\frac{11}{204}\right)$	$e\left(\frac{61}{102}\right)$
$\chi_{10003}(32,\cdot)$	10003.cr	84	yes	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{10003}(33,\cdot)$	10003.el	1428	yes	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{106}{357}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{155}{714}\right)$	$e\left(\frac{1291}{1428}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{212}{357}\right)$	$e\left(\frac{1177}{1428}\right)$	$e\left(\frac{19}{1428}\right)$	$e\left(\frac{365}{714}\right)$
$\chi_{10003}(34,\cdot)$	10003.dv	476	yes	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{88}{119}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{95}{238}\right)$	$e\left(\frac{369}{476}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{57}{119}\right)$	$e\left(\frac{207}{476}\right)$	$e\left(\frac{265}{476}\right)$	$e\left(\frac{193}{238}\right)$
$\chi_{10003}(36,\cdot)$	10003.dz	714	no	$1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{94}{357}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{39}{119}\right)$	$e\left(\frac{1}{714}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{188}{357}\right)$	$e\left(\frac{47}{714}\right)$	$e\left(\frac{389}{714}\right)$	$e\left(\frac{88}{119}\right)$
$\chi_{10003}(37,\cdot)$	10003.em	1428	yes	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{709}{714}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{214}{357}\right)$	$e\left(\frac{365}{476}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{352}{357}\right)$	$e\left(\frac{533}{1428}\right)$	$e\left(\frac{173}{1428}\right)$	$e\left(\frac{193}{357}\right)$

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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	$10003$
Structure	\(C_{6}\times C_{1428}\)
Order	$8568$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{10003}(1,\cdot)\)	10003.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10003}(2,\cdot)\)	10003.cr	84	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{10003}(3,\cdot)\)	10003.eh	714	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{655}{714}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{457}{714}\right)\)	\(e\left(\frac{47}{357}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{298}{357}\right)\)	\(e\left(\frac{305}{357}\right)\)	\(e\left(\frac{271}{714}\right)\)	\(e\left(\frac{247}{714}\right)\)
\(\chi_{10003}(4,\cdot)\)	10003.bt	42	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{10003}(5,\cdot)\)	10003.ef	714	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{457}{714}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{365}{714}\right)\)	\(e\left(\frac{39}{238}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{100}{357}\right)\)	\(e\left(\frac{25}{714}\right)\)	\(e\left(\frac{206}{357}\right)\)	\(e\left(\frac{491}{714}\right)\)
\(\chi_{10003}(6,\cdot)\)	10003.ej	1428	yes	\(1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{47}{357}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{39}{238}\right)\)	\(e\left(\frac{715}{1428}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{94}{357}\right)\)	\(e\left(\frac{761}{1428}\right)\)	\(e\left(\frac{1103}{1428}\right)\)	\(e\left(\frac{207}{238}\right)\)
\(\chi_{10003}(8,\cdot)\)	10003.bo	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{10003}(9,\cdot)\)	10003.dq	357	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{298}{357}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{100}{357}\right)\)	\(e\left(\frac{94}{357}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{239}{357}\right)\)	\(e\left(\frac{253}{357}\right)\)	\(e\left(\frac{271}{357}\right)\)	\(e\left(\frac{247}{357}\right)\)
\(\chi_{10003}(10,\cdot)\)	10003.el	1428	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{305}{357}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{714}\right)\)	\(e\left(\frac{761}{1428}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{253}{357}\right)\)	\(e\left(\frac{1019}{1428}\right)\)	\(e\left(\frac{1385}{1428}\right)\)	\(e\left(\frac{151}{714}\right)\)
\(\chi_{10003}(11,\cdot)\)	10003.eo	1428	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{271}{714}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{206}{357}\right)\)	\(e\left(\frac{1103}{1428}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{271}{357}\right)\)	\(e\left(\frac{1385}{1428}\right)\)	\(e\left(\frac{905}{1428}\right)\)	\(e\left(\frac{59}{357}\right)\)
\(\chi_{10003}(12,\cdot)\)	10003.ef	714	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{247}{714}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{491}{714}\right)\)	\(e\left(\frac{207}{238}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{247}{357}\right)\)	\(e\left(\frac{151}{714}\right)\)	\(e\left(\frac{59}{357}\right)\)	\(e\left(\frac{281}{714}\right)\)
\(\chi_{10003}(13,\cdot)\)	10003.ea	714	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{71}{714}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{238}\right)\)	\(e\left(\frac{248}{357}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{71}{357}\right)\)	\(e\left(\frac{232}{357}\right)\)	\(e\left(\frac{521}{714}\right)\)	\(e\left(\frac{69}{238}\right)\)
\(\chi_{10003}(15,\cdot)\)	10003.dz	714	no	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{199}{357}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{18}{119}\right)\)	\(e\left(\frac{211}{714}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{41}{357}\right)\)	\(e\left(\frac{635}{714}\right)\)	\(e\left(\frac{683}{714}\right)\)	\(e\left(\frac{4}{119}\right)\)
\(\chi_{10003}(16,\cdot)\)	10003.bk	21	yes	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{10003}(17,\cdot)\)	10003.dx	714	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{125}{238}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{625}{714}\right)\)	\(e\left(\frac{145}{357}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{119}\right)\)	\(e\left(\frac{90}{119}\right)\)	\(e\left(\frac{39}{238}\right)\)	\(e\left(\frac{205}{714}\right)\)
\(\chi_{10003}(18,\cdot)\)	10003.di	204	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{102}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{41}{51}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(-i\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{31}{204}\right)\)	\(e\left(\frac{11}{51}\right)\)
\(\chi_{10003}(19,\cdot)\)	10003.dx	714	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{238}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{275}{714}\right)\)	\(e\left(\frac{278}{357}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{55}{119}\right)\)	\(e\left(\frac{111}{119}\right)\)	\(e\left(\frac{179}{238}\right)\)	\(e\left(\frac{233}{714}\right)\)
\(\chi_{10003}(20,\cdot)\)	10003.cz	102	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{102}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{46}{51}\right)\)	\(-1\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{20}{51}\right)\)	\(e\left(\frac{37}{102}\right)\)	\(e\left(\frac{25}{34}\right)\)
\(\chi_{10003}(22,\cdot)\)	10003.dz	714	no	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{212}{357}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{12}{119}\right)\)	\(e\left(\frac{101}{714}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{67}{357}\right)\)	\(e\left(\frac{463}{714}\right)\)	\(e\left(\frac{19}{714}\right)\)	\(e\left(\frac{82}{119}\right)\)
\(\chi_{10003}(23,\cdot)\)	10003.eg	714	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{97}{357}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{241}{357}\right)\)	\(e\left(\frac{653}{714}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{194}{357}\right)\)	\(e\left(\frac{227}{714}\right)\)	\(e\left(\frac{71}{714}\right)\)	\(e\left(\frac{199}{357}\right)\)
\(\chi_{10003}(24,\cdot)\)	10003.el	1428	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{200}{357}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{151}{714}\right)\)	\(e\left(\frac{341}{1428}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{43}{357}\right)\)	\(e\left(\frac{1271}{1428}\right)\)	\(e\left(\frac{797}{1428}\right)\)	\(e\left(\frac{655}{714}\right)\)
\(\chi_{10003}(25,\cdot)\)	10003.dr	357	yes	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{100}{357}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{8}{357}\right)\)	\(e\left(\frac{39}{119}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{200}{357}\right)\)	\(e\left(\frac{25}{357}\right)\)	\(e\left(\frac{55}{357}\right)\)	\(e\left(\frac{134}{357}\right)\)
\(\chi_{10003}(26,\cdot)\)	10003.dj	204	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{16}{51}\right)\)	\(-1\)	\(e\left(\frac{59}{102}\right)\)	\(e\left(\frac{13}{204}\right)\)	\(i\)	\(e\left(\frac{32}{51}\right)\)	\(e\left(\frac{67}{204}\right)\)	\(e\left(\frac{25}{204}\right)\)	\(e\left(\frac{83}{102}\right)\)
\(\chi_{10003}(27,\cdot)\)	10003.do	238	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{179}{238}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{219}{238}\right)\)	\(e\left(\frac{47}{119}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{60}{119}\right)\)	\(e\left(\frac{67}{119}\right)\)	\(e\left(\frac{33}{238}\right)\)	\(e\left(\frac{9}{238}\right)\)
\(\chi_{10003}(29,\cdot)\)	10003.en	1428	no	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{275}{714}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{83}{119}\right)\)	\(e\left(\frac{227}{1428}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{275}{357}\right)\)	\(e\left(\frac{673}{1428}\right)\)	\(e\left(\frac{481}{1428}\right)\)	\(e\left(\frac{111}{119}\right)\)
\(\chi_{10003}(30,\cdot)\)	10003.eo	1428	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{551}{714}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{241}{357}\right)\)	\(e\left(\frac{949}{1428}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{194}{357}\right)\)	\(e\left(\frac{811}{1428}\right)\)	\(e\left(\frac{499}{1428}\right)\)	\(e\left(\frac{199}{357}\right)\)
\(\chi_{10003}(31,\cdot)\)	10003.dj	204	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{5}{51}\right)\)	\(-1\)	\(e\left(\frac{79}{102}\right)\)	\(e\left(\frac{71}{204}\right)\)	\(-i\)	\(e\left(\frac{10}{51}\right)\)	\(e\left(\frac{5}{204}\right)\)	\(e\left(\frac{11}{204}\right)\)	\(e\left(\frac{61}{102}\right)\)
\(\chi_{10003}(32,\cdot)\)	10003.cr	84	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{10003}(33,\cdot)\)	10003.el	1428	yes	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{106}{357}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{155}{714}\right)\)	\(e\left(\frac{1291}{1428}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{212}{357}\right)\)	\(e\left(\frac{1177}{1428}\right)\)	\(e\left(\frac{19}{1428}\right)\)	\(e\left(\frac{365}{714}\right)\)
\(\chi_{10003}(34,\cdot)\)	10003.dv	476	yes	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{88}{119}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{95}{238}\right)\)	\(e\left(\frac{369}{476}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{57}{119}\right)\)	\(e\left(\frac{207}{476}\right)\)	\(e\left(\frac{265}{476}\right)\)	\(e\left(\frac{193}{238}\right)\)
\(\chi_{10003}(36,\cdot)\)	10003.dz	714	no	\(1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{94}{357}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{39}{119}\right)\)	\(e\left(\frac{1}{714}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{188}{357}\right)\)	\(e\left(\frac{47}{714}\right)\)	\(e\left(\frac{389}{714}\right)\)	\(e\left(\frac{88}{119}\right)\)
\(\chi_{10003}(37,\cdot)\)	10003.em	1428	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{709}{714}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{214}{357}\right)\)	\(e\left(\frac{365}{476}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{352}{357}\right)\)	\(e\left(\frac{533}{1428}\right)\)	\(e\left(\frac{173}{1428}\right)\)	\(e\left(\frac{193}{357}\right)\)

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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.