LMFDB - Group of Dirichlet characters of modulus 7031

Show commands: PariGP / SageMath

sage: H = DirichletGroup(7031)

pari: g = idealstar(,7031,2)

Character group

sage: G.order() pari: g.no
Order	=	6864
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{3432}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{7031}(1425,\cdot)$, $\chi_{7031}(5610,\cdot)$

First 32 of 6864 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{7031}(1,\cdot)$	7031.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{7031}(2,\cdot)$	7031.ca	429	yes	$1$	$1$	$e\left(\frac{49}{429}\right)$	$e\left(\frac{100}{429}\right)$	$e\left(\frac{98}{429}\right)$	$e\left(\frac{389}{429}\right)$	$e\left(\frac{149}{429}\right)$	$e\left(\frac{191}{429}\right)$	$e\left(\frac{49}{143}\right)$	$e\left(\frac{200}{429}\right)$	$e\left(\frac{3}{143}\right)$	$e\left(\frac{326}{429}\right)$
$\chi_{7031}(3,\cdot)$	7031.cl	3432	yes	$1$	$1$	$e\left(\frac{100}{429}\right)$	$e\left(\frac{83}{3432}\right)$	$e\left(\frac{200}{429}\right)$	$e\left(\frac{1013}{1716}\right)$	$e\left(\frac{883}{3432}\right)$	$e\left(\frac{2059}{3432}\right)$	$e\left(\frac{100}{143}\right)$	$e\left(\frac{83}{1716}\right)$	$e\left(\frac{471}{572}\right)$	$e\left(\frac{709}{858}\right)$
$\chi_{7031}(4,\cdot)$	7031.ca	429	yes	$1$	$1$	$e\left(\frac{98}{429}\right)$	$e\left(\frac{200}{429}\right)$	$e\left(\frac{196}{429}\right)$	$e\left(\frac{349}{429}\right)$	$e\left(\frac{298}{429}\right)$	$e\left(\frac{382}{429}\right)$	$e\left(\frac{98}{143}\right)$	$e\left(\frac{400}{429}\right)$	$e\left(\frac{6}{143}\right)$	$e\left(\frac{223}{429}\right)$
$\chi_{7031}(5,\cdot)$	7031.ci	1716	yes	$1$	$1$	$e\left(\frac{389}{429}\right)$	$e\left(\frac{1013}{1716}\right)$	$e\left(\frac{349}{429}\right)$	$e\left(\frac{827}{858}\right)$	$e\left(\frac{853}{1716}\right)$	$e\left(\frac{961}{1716}\right)$	$e\left(\frac{103}{143}\right)$	$e\left(\frac{155}{858}\right)$	$e\left(\frac{249}{286}\right)$	$e\left(\frac{373}{429}\right)$
$\chi_{7031}(6,\cdot)$	7031.cl	3432	yes	$1$	$1$	$e\left(\frac{149}{429}\right)$	$e\left(\frac{883}{3432}\right)$	$e\left(\frac{298}{429}\right)$	$e\left(\frac{853}{1716}\right)$	$e\left(\frac{2075}{3432}\right)$	$e\left(\frac{155}{3432}\right)$	$e\left(\frac{6}{143}\right)$	$e\left(\frac{883}{1716}\right)$	$e\left(\frac{483}{572}\right)$	$e\left(\frac{503}{858}\right)$
$\chi_{7031}(7,\cdot)$	7031.cl	3432	yes	$1$	$1$	$e\left(\frac{191}{429}\right)$	$e\left(\frac{2059}{3432}\right)$	$e\left(\frac{382}{429}\right)$	$e\left(\frac{961}{1716}\right)$	$e\left(\frac{155}{3432}\right)$	$e\left(\frac{1955}{3432}\right)$	$e\left(\frac{48}{143}\right)$	$e\left(\frac{343}{1716}\right)$	$e\left(\frac{3}{572}\right)$	$e\left(\frac{449}{858}\right)$
$\chi_{7031}(8,\cdot)$	7031.bq	143	yes	$1$	$1$	$e\left(\frac{49}{143}\right)$	$e\left(\frac{100}{143}\right)$	$e\left(\frac{98}{143}\right)$	$e\left(\frac{103}{143}\right)$	$e\left(\frac{6}{143}\right)$	$e\left(\frac{48}{143}\right)$	$e\left(\frac{4}{143}\right)$	$e\left(\frac{57}{143}\right)$	$e\left(\frac{9}{143}\right)$	$e\left(\frac{40}{143}\right)$
$\chi_{7031}(9,\cdot)$	7031.ci	1716	yes	$1$	$1$	$e\left(\frac{200}{429}\right)$	$e\left(\frac{83}{1716}\right)$	$e\left(\frac{400}{429}\right)$	$e\left(\frac{155}{858}\right)$	$e\left(\frac{883}{1716}\right)$	$e\left(\frac{343}{1716}\right)$	$e\left(\frac{57}{143}\right)$	$e\left(\frac{83}{858}\right)$	$e\left(\frac{185}{286}\right)$	$e\left(\frac{280}{429}\right)$
$\chi_{7031}(10,\cdot)$	7031.cb	572	yes	$1$	$1$	$e\left(\frac{3}{143}\right)$	$e\left(\frac{471}{572}\right)$	$e\left(\frac{6}{143}\right)$	$e\left(\frac{249}{286}\right)$	$e\left(\frac{483}{572}\right)$	$e\left(\frac{3}{572}\right)$	$e\left(\frac{9}{143}\right)$	$e\left(\frac{185}{286}\right)$	$e\left(\frac{255}{286}\right)$	$e\left(\frac{90}{143}\right)$
$\chi_{7031}(11,\cdot)$	7031.cf	858	yes	$1$	$1$	$e\left(\frac{326}{429}\right)$	$e\left(\frac{709}{858}\right)$	$e\left(\frac{223}{429}\right)$	$e\left(\frac{373}{429}\right)$	$e\left(\frac{503}{858}\right)$	$e\left(\frac{449}{858}\right)$	$e\left(\frac{40}{143}\right)$	$e\left(\frac{280}{429}\right)$	$e\left(\frac{90}{143}\right)$	$e\left(\frac{199}{429}\right)$
$\chi_{7031}(12,\cdot)$	7031.bn	104	yes	$1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{99}{104}\right)$	$e\left(\frac{51}{104}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{7031}(13,\cdot)$	7031.ck	3432	yes	$-1$	$1$	$e\left(\frac{397}{429}\right)$	$e\left(\frac{2393}{3432}\right)$	$e\left(\frac{365}{429}\right)$	$e\left(\frac{551}{1716}\right)$	$e\left(\frac{2137}{3432}\right)$	$e\left(\frac{937}{3432}\right)$	$e\left(\frac{111}{143}\right)$	$e\left(\frac{677}{1716}\right)$	$e\left(\frac{141}{572}\right)$	$e\left(\frac{511}{858}\right)$
$\chi_{7031}(14,\cdot)$	7031.cg	1144	yes	$1$	$1$	$e\left(\frac{80}{143}\right)$	$e\left(\frac{953}{1144}\right)$	$e\left(\frac{17}{143}\right)$	$e\left(\frac{267}{572}\right)$	$e\left(\frac{449}{1144}\right)$	$e\left(\frac{17}{1144}\right)$	$e\left(\frac{97}{143}\right)$	$e\left(\frac{381}{572}\right)$	$e\left(\frac{15}{572}\right)$	$e\left(\frac{81}{286}\right)$
$\chi_{7031}(15,\cdot)$	7031.cg	1144	yes	$1$	$1$	$e\left(\frac{20}{143}\right)$	$e\left(\frac{703}{1144}\right)$	$e\left(\frac{40}{143}\right)$	$e\left(\frac{317}{572}\right)$	$e\left(\frac{863}{1144}\right)$	$e\left(\frac{183}{1144}\right)$	$e\left(\frac{60}{143}\right)$	$e\left(\frac{131}{572}\right)$	$e\left(\frac{397}{572}\right)$	$e\left(\frac{199}{286}\right)$
$\chi_{7031}(16,\cdot)$	7031.ca	429	yes	$1$	$1$	$e\left(\frac{196}{429}\right)$	$e\left(\frac{400}{429}\right)$	$e\left(\frac{392}{429}\right)$	$e\left(\frac{269}{429}\right)$	$e\left(\frac{167}{429}\right)$	$e\left(\frac{335}{429}\right)$	$e\left(\frac{53}{143}\right)$	$e\left(\frac{371}{429}\right)$	$e\left(\frac{12}{143}\right)$	$e\left(\frac{17}{429}\right)$
$\chi_{7031}(17,\cdot)$	7031.cc	572	yes	$-1$	$1$	$e\left(\frac{24}{143}\right)$	$e\left(\frac{193}{572}\right)$	$e\left(\frac{48}{143}\right)$	$e\left(\frac{133}{286}\right)$	$e\left(\frac{289}{572}\right)$	$e\left(\frac{453}{572}\right)$	$e\left(\frac{72}{143}\right)$	$e\left(\frac{193}{286}\right)$	$e\left(\frac{181}{286}\right)$	$e\left(\frac{5}{143}\right)$
$\chi_{7031}(18,\cdot)$	7031.cb	572	yes	$1$	$1$	$e\left(\frac{83}{143}\right)$	$e\left(\frac{161}{572}\right)$	$e\left(\frac{23}{143}\right)$	$e\left(\frac{25}{286}\right)$	$e\left(\frac{493}{572}\right)$	$e\left(\frac{369}{572}\right)$	$e\left(\frac{106}{143}\right)$	$e\left(\frac{161}{286}\right)$	$e\left(\frac{191}{286}\right)$	$e\left(\frac{59}{143}\right)$
$\chi_{7031}(19,\cdot)$	7031.ck	3432	yes	$-1$	$1$	$e\left(\frac{2}{429}\right)$	$e\left(\frac{2773}{3432}\right)$	$e\left(\frac{4}{429}\right)$	$e\left(\frac{475}{1716}\right)$	$e\left(\frac{2789}{3432}\right)$	$e\left(\frac{3293}{3432}\right)$	$e\left(\frac{2}{143}\right)$	$e\left(\frac{1057}{1716}\right)$	$e\left(\frac{161}{572}\right)$	$e\left(\frac{263}{858}\right)$
$\chi_{7031}(20,\cdot)$	7031.ci	1716	yes	$1$	$1$	$e\left(\frac{58}{429}\right)$	$e\left(\frac{97}{1716}\right)$	$e\left(\frac{116}{429}\right)$	$e\left(\frac{667}{858}\right)$	$e\left(\frac{329}{1716}\right)$	$e\left(\frac{773}{1716}\right)$	$e\left(\frac{58}{143}\right)$	$e\left(\frac{97}{858}\right)$	$e\left(\frac{261}{286}\right)$	$e\left(\frac{167}{429}\right)$
$\chi_{7031}(21,\cdot)$	7031.cb	572	yes	$1$	$1$	$e\left(\frac{97}{143}\right)$	$e\left(\frac{357}{572}\right)$	$e\left(\frac{51}{143}\right)$	$e\left(\frac{43}{286}\right)$	$e\left(\frac{173}{572}\right)$	$e\left(\frac{97}{572}\right)$	$e\left(\frac{5}{143}\right)$	$e\left(\frac{71}{286}\right)$	$e\left(\frac{237}{286}\right)$	$e\left(\frac{50}{143}\right)$
$\chi_{7031}(22,\cdot)$	7031.bv	286	yes	$1$	$1$	$e\left(\frac{125}{143}\right)$	$e\left(\frac{17}{286}\right)$	$e\left(\frac{107}{143}\right)$	$e\left(\frac{111}{143}\right)$	$e\left(\frac{267}{286}\right)$	$e\left(\frac{277}{286}\right)$	$e\left(\frac{89}{143}\right)$	$e\left(\frac{17}{143}\right)$	$e\left(\frac{93}{143}\right)$	$e\left(\frac{32}{143}\right)$
$\chi_{7031}(23,\cdot)$	7031.bu	264	yes	$-1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{259}{264}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{179}{264}\right)$	$e\left(\frac{35}{264}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{127}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{66}\right)$
$\chi_{7031}(24,\cdot)$	7031.bt	264	yes	$1$	$1$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{191}{264}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{247}{264}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{7031}(25,\cdot)$	7031.cf	858	yes	$1$	$1$	$e\left(\frac{349}{429}\right)$	$e\left(\frac{155}{858}\right)$	$e\left(\frac{269}{429}\right)$	$e\left(\frac{398}{429}\right)$	$e\left(\frac{853}{858}\right)$	$e\left(\frac{103}{858}\right)$	$e\left(\frac{63}{143}\right)$	$e\left(\frac{155}{429}\right)$	$e\left(\frac{106}{143}\right)$	$e\left(\frac{317}{429}\right)$
$\chi_{7031}(26,\cdot)$	7031.ck	3432	yes	$-1$	$1$	$e\left(\frac{17}{429}\right)$	$e\left(\frac{3193}{3432}\right)$	$e\left(\frac{34}{429}\right)$	$e\left(\frac{391}{1716}\right)$	$e\left(\frac{3329}{3432}\right)$	$e\left(\frac{2465}{3432}\right)$	$e\left(\frac{17}{143}\right)$	$e\left(\frac{1477}{1716}\right)$	$e\left(\frac{153}{572}\right)$	$e\left(\frac{305}{858}\right)$
$\chi_{7031}(27,\cdot)$	7031.cg	1144	yes	$1$	$1$	$e\left(\frac{100}{143}\right)$	$e\left(\frac{83}{1144}\right)$	$e\left(\frac{57}{143}\right)$	$e\left(\frac{441}{572}\right)$	$e\left(\frac{883}{1144}\right)$	$e\left(\frac{915}{1144}\right)$	$e\left(\frac{14}{143}\right)$	$e\left(\frac{83}{572}\right)$	$e\left(\frac{269}{572}\right)$	$e\left(\frac{137}{286}\right)$
$\chi_{7031}(28,\cdot)$	7031.cl	3432	yes	$1$	$1$	$e\left(\frac{289}{429}\right)$	$e\left(\frac{227}{3432}\right)$	$e\left(\frac{149}{429}\right)$	$e\left(\frac{641}{1716}\right)$	$e\left(\frac{2539}{3432}\right)$	$e\left(\frac{1579}{3432}\right)$	$e\left(\frac{3}{143}\right)$	$e\left(\frac{227}{1716}\right)$	$e\left(\frac{27}{572}\right)$	$e\left(\frac{37}{858}\right)$
$\chi_{7031}(29,\cdot)$	7031.cl	3432	yes	$1$	$1$	$e\left(\frac{125}{429}\right)$	$e\left(\frac{2785}{3432}\right)$	$e\left(\frac{250}{429}\right)$	$e\left(\frac{1159}{1716}\right)$	$e\left(\frac{353}{3432}\right)$	$e\left(\frac{2681}{3432}\right)$	$e\left(\frac{125}{143}\right)$	$e\left(\frac{1069}{1716}\right)$	$e\left(\frac{553}{572}\right)$	$e\left(\frac{779}{858}\right)$
$\chi_{7031}(30,\cdot)$	7031.cl	3432	yes	$1$	$1$	$e\left(\frac{109}{429}\right)$	$e\left(\frac{2909}{3432}\right)$	$e\left(\frac{218}{429}\right)$	$e\left(\frac{791}{1716}\right)$	$e\left(\frac{349}{3432}\right)$	$e\left(\frac{2077}{3432}\right)$	$e\left(\frac{109}{143}\right)$	$e\left(\frac{1193}{1716}\right)$	$e\left(\frac{409}{572}\right)$	$e\left(\frac{391}{858}\right)$
$\chi_{7031}(31,\cdot)$	7031.ck	3432	yes	$-1$	$1$	$e\left(\frac{218}{429}\right)$	$e\left(\frac{241}{3432}\right)$	$e\left(\frac{7}{429}\right)$	$e\left(\frac{295}{1716}\right)$	$e\left(\frac{1985}{3432}\right)$	$e\left(\frac{2009}{3432}\right)$	$e\left(\frac{75}{143}\right)$	$e\left(\frac{241}{1716}\right)$	$e\left(\frac{389}{572}\right)$	$e\left(\frac{353}{858}\right)$
$\chi_{7031}(32,\cdot)$	7031.ca	429	yes	$1$	$1$	$e\left(\frac{245}{429}\right)$	$e\left(\frac{71}{429}\right)$	$e\left(\frac{61}{429}\right)$	$e\left(\frac{229}{429}\right)$	$e\left(\frac{316}{429}\right)$	$e\left(\frac{97}{429}\right)$	$e\left(\frac{102}{143}\right)$	$e\left(\frac{142}{429}\right)$	$e\left(\frac{15}{143}\right)$	$e\left(\frac{343}{429}\right)$

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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	$7031$
Structure	\(C_{2}\times C_{3432}\)
Order	$6864$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{7031}(1,\cdot)\)	7031.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{7031}(2,\cdot)\)	7031.ca	429	yes	\(1\)	\(1\)	\(e\left(\frac{49}{429}\right)\)	\(e\left(\frac{100}{429}\right)\)	\(e\left(\frac{98}{429}\right)\)	\(e\left(\frac{389}{429}\right)\)	\(e\left(\frac{149}{429}\right)\)	\(e\left(\frac{191}{429}\right)\)	\(e\left(\frac{49}{143}\right)\)	\(e\left(\frac{200}{429}\right)\)	\(e\left(\frac{3}{143}\right)\)	\(e\left(\frac{326}{429}\right)\)
\(\chi_{7031}(3,\cdot)\)	7031.cl	3432	yes	\(1\)	\(1\)	\(e\left(\frac{100}{429}\right)\)	\(e\left(\frac{83}{3432}\right)\)	\(e\left(\frac{200}{429}\right)\)	\(e\left(\frac{1013}{1716}\right)\)	\(e\left(\frac{883}{3432}\right)\)	\(e\left(\frac{2059}{3432}\right)\)	\(e\left(\frac{100}{143}\right)\)	\(e\left(\frac{83}{1716}\right)\)	\(e\left(\frac{471}{572}\right)\)	\(e\left(\frac{709}{858}\right)\)
\(\chi_{7031}(4,\cdot)\)	7031.ca	429	yes	\(1\)	\(1\)	\(e\left(\frac{98}{429}\right)\)	\(e\left(\frac{200}{429}\right)\)	\(e\left(\frac{196}{429}\right)\)	\(e\left(\frac{349}{429}\right)\)	\(e\left(\frac{298}{429}\right)\)	\(e\left(\frac{382}{429}\right)\)	\(e\left(\frac{98}{143}\right)\)	\(e\left(\frac{400}{429}\right)\)	\(e\left(\frac{6}{143}\right)\)	\(e\left(\frac{223}{429}\right)\)
\(\chi_{7031}(5,\cdot)\)	7031.ci	1716	yes	\(1\)	\(1\)	\(e\left(\frac{389}{429}\right)\)	\(e\left(\frac{1013}{1716}\right)\)	\(e\left(\frac{349}{429}\right)\)	\(e\left(\frac{827}{858}\right)\)	\(e\left(\frac{853}{1716}\right)\)	\(e\left(\frac{961}{1716}\right)\)	\(e\left(\frac{103}{143}\right)\)	\(e\left(\frac{155}{858}\right)\)	\(e\left(\frac{249}{286}\right)\)	\(e\left(\frac{373}{429}\right)\)
\(\chi_{7031}(6,\cdot)\)	7031.cl	3432	yes	\(1\)	\(1\)	\(e\left(\frac{149}{429}\right)\)	\(e\left(\frac{883}{3432}\right)\)	\(e\left(\frac{298}{429}\right)\)	\(e\left(\frac{853}{1716}\right)\)	\(e\left(\frac{2075}{3432}\right)\)	\(e\left(\frac{155}{3432}\right)\)	\(e\left(\frac{6}{143}\right)\)	\(e\left(\frac{883}{1716}\right)\)	\(e\left(\frac{483}{572}\right)\)	\(e\left(\frac{503}{858}\right)\)
\(\chi_{7031}(7,\cdot)\)	7031.cl	3432	yes	\(1\)	\(1\)	\(e\left(\frac{191}{429}\right)\)	\(e\left(\frac{2059}{3432}\right)\)	\(e\left(\frac{382}{429}\right)\)	\(e\left(\frac{961}{1716}\right)\)	\(e\left(\frac{155}{3432}\right)\)	\(e\left(\frac{1955}{3432}\right)\)	\(e\left(\frac{48}{143}\right)\)	\(e\left(\frac{343}{1716}\right)\)	\(e\left(\frac{3}{572}\right)\)	\(e\left(\frac{449}{858}\right)\)
\(\chi_{7031}(8,\cdot)\)	7031.bq	143	yes	\(1\)	\(1\)	\(e\left(\frac{49}{143}\right)\)	\(e\left(\frac{100}{143}\right)\)	\(e\left(\frac{98}{143}\right)\)	\(e\left(\frac{103}{143}\right)\)	\(e\left(\frac{6}{143}\right)\)	\(e\left(\frac{48}{143}\right)\)	\(e\left(\frac{4}{143}\right)\)	\(e\left(\frac{57}{143}\right)\)	\(e\left(\frac{9}{143}\right)\)	\(e\left(\frac{40}{143}\right)\)
\(\chi_{7031}(9,\cdot)\)	7031.ci	1716	yes	\(1\)	\(1\)	\(e\left(\frac{200}{429}\right)\)	\(e\left(\frac{83}{1716}\right)\)	\(e\left(\frac{400}{429}\right)\)	\(e\left(\frac{155}{858}\right)\)	\(e\left(\frac{883}{1716}\right)\)	\(e\left(\frac{343}{1716}\right)\)	\(e\left(\frac{57}{143}\right)\)	\(e\left(\frac{83}{858}\right)\)	\(e\left(\frac{185}{286}\right)\)	\(e\left(\frac{280}{429}\right)\)
\(\chi_{7031}(10,\cdot)\)	7031.cb	572	yes	\(1\)	\(1\)	\(e\left(\frac{3}{143}\right)\)	\(e\left(\frac{471}{572}\right)\)	\(e\left(\frac{6}{143}\right)\)	\(e\left(\frac{249}{286}\right)\)	\(e\left(\frac{483}{572}\right)\)	\(e\left(\frac{3}{572}\right)\)	\(e\left(\frac{9}{143}\right)\)	\(e\left(\frac{185}{286}\right)\)	\(e\left(\frac{255}{286}\right)\)	\(e\left(\frac{90}{143}\right)\)
\(\chi_{7031}(11,\cdot)\)	7031.cf	858	yes	\(1\)	\(1\)	\(e\left(\frac{326}{429}\right)\)	\(e\left(\frac{709}{858}\right)\)	\(e\left(\frac{223}{429}\right)\)	\(e\left(\frac{373}{429}\right)\)	\(e\left(\frac{503}{858}\right)\)	\(e\left(\frac{449}{858}\right)\)	\(e\left(\frac{40}{143}\right)\)	\(e\left(\frac{280}{429}\right)\)	\(e\left(\frac{90}{143}\right)\)	\(e\left(\frac{199}{429}\right)\)
\(\chi_{7031}(12,\cdot)\)	7031.bn	104	yes	\(1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{99}{104}\right)\)	\(e\left(\frac{51}{104}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{7031}(13,\cdot)\)	7031.ck	3432	yes	\(-1\)	\(1\)	\(e\left(\frac{397}{429}\right)\)	\(e\left(\frac{2393}{3432}\right)\)	\(e\left(\frac{365}{429}\right)\)	\(e\left(\frac{551}{1716}\right)\)	\(e\left(\frac{2137}{3432}\right)\)	\(e\left(\frac{937}{3432}\right)\)	\(e\left(\frac{111}{143}\right)\)	\(e\left(\frac{677}{1716}\right)\)	\(e\left(\frac{141}{572}\right)\)	\(e\left(\frac{511}{858}\right)\)
\(\chi_{7031}(14,\cdot)\)	7031.cg	1144	yes	\(1\)	\(1\)	\(e\left(\frac{80}{143}\right)\)	\(e\left(\frac{953}{1144}\right)\)	\(e\left(\frac{17}{143}\right)\)	\(e\left(\frac{267}{572}\right)\)	\(e\left(\frac{449}{1144}\right)\)	\(e\left(\frac{17}{1144}\right)\)	\(e\left(\frac{97}{143}\right)\)	\(e\left(\frac{381}{572}\right)\)	\(e\left(\frac{15}{572}\right)\)	\(e\left(\frac{81}{286}\right)\)
\(\chi_{7031}(15,\cdot)\)	7031.cg	1144	yes	\(1\)	\(1\)	\(e\left(\frac{20}{143}\right)\)	\(e\left(\frac{703}{1144}\right)\)	\(e\left(\frac{40}{143}\right)\)	\(e\left(\frac{317}{572}\right)\)	\(e\left(\frac{863}{1144}\right)\)	\(e\left(\frac{183}{1144}\right)\)	\(e\left(\frac{60}{143}\right)\)	\(e\left(\frac{131}{572}\right)\)	\(e\left(\frac{397}{572}\right)\)	\(e\left(\frac{199}{286}\right)\)
\(\chi_{7031}(16,\cdot)\)	7031.ca	429	yes	\(1\)	\(1\)	\(e\left(\frac{196}{429}\right)\)	\(e\left(\frac{400}{429}\right)\)	\(e\left(\frac{392}{429}\right)\)	\(e\left(\frac{269}{429}\right)\)	\(e\left(\frac{167}{429}\right)\)	\(e\left(\frac{335}{429}\right)\)	\(e\left(\frac{53}{143}\right)\)	\(e\left(\frac{371}{429}\right)\)	\(e\left(\frac{12}{143}\right)\)	\(e\left(\frac{17}{429}\right)\)
\(\chi_{7031}(17,\cdot)\)	7031.cc	572	yes	\(-1\)	\(1\)	\(e\left(\frac{24}{143}\right)\)	\(e\left(\frac{193}{572}\right)\)	\(e\left(\frac{48}{143}\right)\)	\(e\left(\frac{133}{286}\right)\)	\(e\left(\frac{289}{572}\right)\)	\(e\left(\frac{453}{572}\right)\)	\(e\left(\frac{72}{143}\right)\)	\(e\left(\frac{193}{286}\right)\)	\(e\left(\frac{181}{286}\right)\)	\(e\left(\frac{5}{143}\right)\)
\(\chi_{7031}(18,\cdot)\)	7031.cb	572	yes	\(1\)	\(1\)	\(e\left(\frac{83}{143}\right)\)	\(e\left(\frac{161}{572}\right)\)	\(e\left(\frac{23}{143}\right)\)	\(e\left(\frac{25}{286}\right)\)	\(e\left(\frac{493}{572}\right)\)	\(e\left(\frac{369}{572}\right)\)	\(e\left(\frac{106}{143}\right)\)	\(e\left(\frac{161}{286}\right)\)	\(e\left(\frac{191}{286}\right)\)	\(e\left(\frac{59}{143}\right)\)
\(\chi_{7031}(19,\cdot)\)	7031.ck	3432	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{429}\right)\)	\(e\left(\frac{2773}{3432}\right)\)	\(e\left(\frac{4}{429}\right)\)	\(e\left(\frac{475}{1716}\right)\)	\(e\left(\frac{2789}{3432}\right)\)	\(e\left(\frac{3293}{3432}\right)\)	\(e\left(\frac{2}{143}\right)\)	\(e\left(\frac{1057}{1716}\right)\)	\(e\left(\frac{161}{572}\right)\)	\(e\left(\frac{263}{858}\right)\)
\(\chi_{7031}(20,\cdot)\)	7031.ci	1716	yes	\(1\)	\(1\)	\(e\left(\frac{58}{429}\right)\)	\(e\left(\frac{97}{1716}\right)\)	\(e\left(\frac{116}{429}\right)\)	\(e\left(\frac{667}{858}\right)\)	\(e\left(\frac{329}{1716}\right)\)	\(e\left(\frac{773}{1716}\right)\)	\(e\left(\frac{58}{143}\right)\)	\(e\left(\frac{97}{858}\right)\)	\(e\left(\frac{261}{286}\right)\)	\(e\left(\frac{167}{429}\right)\)
\(\chi_{7031}(21,\cdot)\)	7031.cb	572	yes	\(1\)	\(1\)	\(e\left(\frac{97}{143}\right)\)	\(e\left(\frac{357}{572}\right)\)	\(e\left(\frac{51}{143}\right)\)	\(e\left(\frac{43}{286}\right)\)	\(e\left(\frac{173}{572}\right)\)	\(e\left(\frac{97}{572}\right)\)	\(e\left(\frac{5}{143}\right)\)	\(e\left(\frac{71}{286}\right)\)	\(e\left(\frac{237}{286}\right)\)	\(e\left(\frac{50}{143}\right)\)
\(\chi_{7031}(22,\cdot)\)	7031.bv	286	yes	\(1\)	\(1\)	\(e\left(\frac{125}{143}\right)\)	\(e\left(\frac{17}{286}\right)\)	\(e\left(\frac{107}{143}\right)\)	\(e\left(\frac{111}{143}\right)\)	\(e\left(\frac{267}{286}\right)\)	\(e\left(\frac{277}{286}\right)\)	\(e\left(\frac{89}{143}\right)\)	\(e\left(\frac{17}{143}\right)\)	\(e\left(\frac{93}{143}\right)\)	\(e\left(\frac{32}{143}\right)\)
\(\chi_{7031}(23,\cdot)\)	7031.bu	264	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{259}{264}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{179}{264}\right)\)	\(e\left(\frac{35}{264}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{127}{132}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{66}\right)\)
\(\chi_{7031}(24,\cdot)\)	7031.bt	264	yes	\(1\)	\(1\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{191}{264}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{247}{264}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{7031}(25,\cdot)\)	7031.cf	858	yes	\(1\)	\(1\)	\(e\left(\frac{349}{429}\right)\)	\(e\left(\frac{155}{858}\right)\)	\(e\left(\frac{269}{429}\right)\)	\(e\left(\frac{398}{429}\right)\)	\(e\left(\frac{853}{858}\right)\)	\(e\left(\frac{103}{858}\right)\)	\(e\left(\frac{63}{143}\right)\)	\(e\left(\frac{155}{429}\right)\)	\(e\left(\frac{106}{143}\right)\)	\(e\left(\frac{317}{429}\right)\)
\(\chi_{7031}(26,\cdot)\)	7031.ck	3432	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{429}\right)\)	\(e\left(\frac{3193}{3432}\right)\)	\(e\left(\frac{34}{429}\right)\)	\(e\left(\frac{391}{1716}\right)\)	\(e\left(\frac{3329}{3432}\right)\)	\(e\left(\frac{2465}{3432}\right)\)	\(e\left(\frac{17}{143}\right)\)	\(e\left(\frac{1477}{1716}\right)\)	\(e\left(\frac{153}{572}\right)\)	\(e\left(\frac{305}{858}\right)\)
\(\chi_{7031}(27,\cdot)\)	7031.cg	1144	yes	\(1\)	\(1\)	\(e\left(\frac{100}{143}\right)\)	\(e\left(\frac{83}{1144}\right)\)	\(e\left(\frac{57}{143}\right)\)	\(e\left(\frac{441}{572}\right)\)	\(e\left(\frac{883}{1144}\right)\)	\(e\left(\frac{915}{1144}\right)\)	\(e\left(\frac{14}{143}\right)\)	\(e\left(\frac{83}{572}\right)\)	\(e\left(\frac{269}{572}\right)\)	\(e\left(\frac{137}{286}\right)\)
\(\chi_{7031}(28,\cdot)\)	7031.cl	3432	yes	\(1\)	\(1\)	\(e\left(\frac{289}{429}\right)\)	\(e\left(\frac{227}{3432}\right)\)	\(e\left(\frac{149}{429}\right)\)	\(e\left(\frac{641}{1716}\right)\)	\(e\left(\frac{2539}{3432}\right)\)	\(e\left(\frac{1579}{3432}\right)\)	\(e\left(\frac{3}{143}\right)\)	\(e\left(\frac{227}{1716}\right)\)	\(e\left(\frac{27}{572}\right)\)	\(e\left(\frac{37}{858}\right)\)
\(\chi_{7031}(29,\cdot)\)	7031.cl	3432	yes	\(1\)	\(1\)	\(e\left(\frac{125}{429}\right)\)	\(e\left(\frac{2785}{3432}\right)\)	\(e\left(\frac{250}{429}\right)\)	\(e\left(\frac{1159}{1716}\right)\)	\(e\left(\frac{353}{3432}\right)\)	\(e\left(\frac{2681}{3432}\right)\)	\(e\left(\frac{125}{143}\right)\)	\(e\left(\frac{1069}{1716}\right)\)	\(e\left(\frac{553}{572}\right)\)	\(e\left(\frac{779}{858}\right)\)
\(\chi_{7031}(30,\cdot)\)	7031.cl	3432	yes	\(1\)	\(1\)	\(e\left(\frac{109}{429}\right)\)	\(e\left(\frac{2909}{3432}\right)\)	\(e\left(\frac{218}{429}\right)\)	\(e\left(\frac{791}{1716}\right)\)	\(e\left(\frac{349}{3432}\right)\)	\(e\left(\frac{2077}{3432}\right)\)	\(e\left(\frac{109}{143}\right)\)	\(e\left(\frac{1193}{1716}\right)\)	\(e\left(\frac{409}{572}\right)\)	\(e\left(\frac{391}{858}\right)\)
\(\chi_{7031}(31,\cdot)\)	7031.ck	3432	yes	\(-1\)	\(1\)	\(e\left(\frac{218}{429}\right)\)	\(e\left(\frac{241}{3432}\right)\)	\(e\left(\frac{7}{429}\right)\)	\(e\left(\frac{295}{1716}\right)\)	\(e\left(\frac{1985}{3432}\right)\)	\(e\left(\frac{2009}{3432}\right)\)	\(e\left(\frac{75}{143}\right)\)	\(e\left(\frac{241}{1716}\right)\)	\(e\left(\frac{389}{572}\right)\)	\(e\left(\frac{353}{858}\right)\)
\(\chi_{7031}(32,\cdot)\)	7031.ca	429	yes	\(1\)	\(1\)	\(e\left(\frac{245}{429}\right)\)	\(e\left(\frac{71}{429}\right)\)	\(e\left(\frac{61}{429}\right)\)	\(e\left(\frac{229}{429}\right)\)	\(e\left(\frac{316}{429}\right)\)	\(e\left(\frac{97}{429}\right)\)	\(e\left(\frac{102}{143}\right)\)	\(e\left(\frac{142}{429}\right)\)	\(e\left(\frac{15}{143}\right)\)	\(e\left(\frac{343}{429}\right)\)

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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.