LMFDB - Group of Dirichlet characters of modulus 4031

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4031)

pari: g = idealstar(,4031,2)

Character group

sage: G.order() pari: g.no
Order	=	3864
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1932}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4031}(3337,\cdot)$, $\chi_{4031}(697,\cdot)$

First 32 of 3864 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4031}(1,\cdot)$	4031.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4031}(2,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{83}{1932}\right)$	$e\left(\frac{919}{1932}\right)$	$e\left(\frac{83}{966}\right)$	$e\left(\frac{395}{966}\right)$	$e\left(\frac{167}{322}\right)$	$e\left(\frac{382}{483}\right)$	$e\left(\frac{83}{644}\right)$	$e\left(\frac{919}{966}\right)$	$e\left(\frac{291}{644}\right)$	$e\left(\frac{857}{1932}\right)$
$\chi_{4031}(3,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{919}{1932}\right)$	$e\left(\frac{143}{1932}\right)$	$e\left(\frac{919}{966}\right)$	$e\left(\frac{463}{966}\right)$	$e\left(\frac{177}{322}\right)$	$e\left(\frac{482}{483}\right)$	$e\left(\frac{275}{644}\right)$	$e\left(\frac{143}{966}\right)$	$e\left(\frac{615}{644}\right)$	$e\left(\frac{85}{1932}\right)$
$\chi_{4031}(4,\cdot)$	4031.bt	966	yes	$1$	$1$	$e\left(\frac{83}{966}\right)$	$e\left(\frac{919}{966}\right)$	$e\left(\frac{83}{483}\right)$	$e\left(\frac{395}{483}\right)$	$e\left(\frac{6}{161}\right)$	$e\left(\frac{281}{483}\right)$	$e\left(\frac{83}{322}\right)$	$e\left(\frac{436}{483}\right)$	$e\left(\frac{291}{322}\right)$	$e\left(\frac{857}{966}\right)$
$\chi_{4031}(5,\cdot)$	4031.bt	966	yes	$1$	$1$	$e\left(\frac{395}{966}\right)$	$e\left(\frac{463}{966}\right)$	$e\left(\frac{395}{483}\right)$	$e\left(\frac{425}{483}\right)$	$e\left(\frac{143}{161}\right)$	$e\left(\frac{284}{483}\right)$	$e\left(\frac{73}{322}\right)$	$e\left(\frac{463}{483}\right)$	$e\left(\frac{93}{322}\right)$	$e\left(\frac{5}{966}\right)$
$\chi_{4031}(6,\cdot)$	4031.bl	322	yes	$1$	$1$	$e\left(\frac{167}{322}\right)$	$e\left(\frac{177}{322}\right)$	$e\left(\frac{6}{161}\right)$	$e\left(\frac{143}{161}\right)$	$e\left(\frac{11}{161}\right)$	$e\left(\frac{127}{161}\right)$	$e\left(\frac{179}{322}\right)$	$e\left(\frac{16}{161}\right)$	$e\left(\frac{131}{322}\right)$	$e\left(\frac{157}{322}\right)$
$\chi_{4031}(7,\cdot)$	4031.bo	483	yes	$1$	$1$	$e\left(\frac{382}{483}\right)$	$e\left(\frac{482}{483}\right)$	$e\left(\frac{281}{483}\right)$	$e\left(\frac{284}{483}\right)$	$e\left(\frac{127}{161}\right)$	$e\left(\frac{125}{483}\right)$	$e\left(\frac{60}{161}\right)$	$e\left(\frac{481}{483}\right)$	$e\left(\frac{61}{161}\right)$	$e\left(\frac{121}{483}\right)$
$\chi_{4031}(8,\cdot)$	4031.bq	644	yes	$1$	$1$	$e\left(\frac{83}{644}\right)$	$e\left(\frac{275}{644}\right)$	$e\left(\frac{83}{322}\right)$	$e\left(\frac{73}{322}\right)$	$e\left(\frac{179}{322}\right)$	$e\left(\frac{60}{161}\right)$	$e\left(\frac{249}{644}\right)$	$e\left(\frac{275}{322}\right)$	$e\left(\frac{229}{644}\right)$	$e\left(\frac{213}{644}\right)$
$\chi_{4031}(9,\cdot)$	4031.bt	966	yes	$1$	$1$	$e\left(\frac{919}{966}\right)$	$e\left(\frac{143}{966}\right)$	$e\left(\frac{436}{483}\right)$	$e\left(\frac{463}{483}\right)$	$e\left(\frac{16}{161}\right)$	$e\left(\frac{481}{483}\right)$	$e\left(\frac{275}{322}\right)$	$e\left(\frac{143}{483}\right)$	$e\left(\frac{293}{322}\right)$	$e\left(\frac{85}{966}\right)$
$\chi_{4031}(10,\cdot)$	4031.bq	644	yes	$1$	$1$	$e\left(\frac{291}{644}\right)$	$e\left(\frac{615}{644}\right)$	$e\left(\frac{291}{322}\right)$	$e\left(\frac{93}{322}\right)$	$e\left(\frac{131}{322}\right)$	$e\left(\frac{61}{161}\right)$	$e\left(\frac{229}{644}\right)$	$e\left(\frac{293}{322}\right)$	$e\left(\frac{477}{644}\right)$	$e\left(\frac{289}{644}\right)$
$\chi_{4031}(11,\cdot)$	4031.bv	1932	yes	$-1$	$1$	$e\left(\frac{857}{1932}\right)$	$e\left(\frac{85}{1932}\right)$	$e\left(\frac{857}{966}\right)$	$e\left(\frac{5}{966}\right)$	$e\left(\frac{157}{322}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{213}{644}\right)$	$e\left(\frac{85}{966}\right)$	$e\left(\frac{289}{644}\right)$	$e\left(\frac{341}{1932}\right)$
$\chi_{4031}(12,\cdot)$	4031.bk	276	yes	$1$	$1$	$e\left(\frac{155}{276}\right)$	$e\left(\frac{7}{276}\right)$	$e\left(\frac{17}{138}\right)$	$e\left(\frac{41}{138}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{257}{276}\right)$
$\chi_{4031}(13,\cdot)$	4031.bt	966	yes	$1$	$1$	$e\left(\frac{103}{966}\right)$	$e\left(\frac{221}{966}\right)$	$e\left(\frac{103}{483}\right)$	$e\left(\frac{13}{483}\right)$	$e\left(\frac{54}{161}\right)$	$e\left(\frac{436}{483}\right)$	$e\left(\frac{103}{322}\right)$	$e\left(\frac{221}{483}\right)$	$e\left(\frac{43}{322}\right)$	$e\left(\frac{307}{966}\right)$
$\chi_{4031}(14,\cdot)$	4031.bq	644	yes	$1$	$1$	$e\left(\frac{537}{644}\right)$	$e\left(\frac{305}{644}\right)$	$e\left(\frac{215}{322}\right)$	$e\left(\frac{321}{322}\right)$	$e\left(\frac{99}{322}\right)$	$e\left(\frac{8}{161}\right)$	$e\left(\frac{323}{644}\right)$	$e\left(\frac{305}{322}\right)$	$e\left(\frac{535}{644}\right)$	$e\left(\frac{447}{644}\right)$
$\chi_{4031}(15,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{1709}{1932}\right)$	$e\left(\frac{1069}{1932}\right)$	$e\left(\frac{743}{966}\right)$	$e\left(\frac{347}{966}\right)$	$e\left(\frac{141}{322}\right)$	$e\left(\frac{283}{483}\right)$	$e\left(\frac{421}{644}\right)$	$e\left(\frac{103}{966}\right)$	$e\left(\frac{157}{644}\right)$	$e\left(\frac{95}{1932}\right)$
$\chi_{4031}(16,\cdot)$	4031.bo	483	yes	$1$	$1$	$e\left(\frac{83}{483}\right)$	$e\left(\frac{436}{483}\right)$	$e\left(\frac{166}{483}\right)$	$e\left(\frac{307}{483}\right)$	$e\left(\frac{12}{161}\right)$	$e\left(\frac{79}{483}\right)$	$e\left(\frac{83}{161}\right)$	$e\left(\frac{389}{483}\right)$	$e\left(\frac{130}{161}\right)$	$e\left(\frac{374}{483}\right)$
$\chi_{4031}(17,\cdot)$	4031.bk	276	yes	$1$	$1$	$e\left(\frac{145}{276}\right)$	$e\left(\frac{149}{276}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{11}{138}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{187}{276}\right)$
$\chi_{4031}(18,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{1921}{1932}\right)$	$e\left(\frac{1205}{1932}\right)$	$e\left(\frac{955}{966}\right)$	$e\left(\frac{355}{966}\right)$	$e\left(\frac{199}{322}\right)$	$e\left(\frac{380}{483}\right)$	$e\left(\frac{633}{644}\right)$	$e\left(\frac{239}{966}\right)$	$e\left(\frac{233}{644}\right)$	$e\left(\frac{1027}{1932}\right)$
$\chi_{4031}(19,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{1475}{1932}\right)$	$e\left(\frac{1411}{1932}\right)$	$e\left(\frac{509}{966}\right)$	$e\left(\frac{83}{966}\right)$	$e\left(\frac{159}{322}\right)$	$e\left(\frac{463}{483}\right)$	$e\left(\frac{187}{644}\right)$	$e\left(\frac{445}{966}\right)$	$e\left(\frac{547}{644}\right)$	$e\left(\frac{1217}{1932}\right)$
$\chi_{4031}(20,\cdot)$	4031.bo	483	yes	$1$	$1$	$e\left(\frac{239}{483}\right)$	$e\left(\frac{208}{483}\right)$	$e\left(\frac{478}{483}\right)$	$e\left(\frac{337}{483}\right)$	$e\left(\frac{149}{161}\right)$	$e\left(\frac{82}{483}\right)$	$e\left(\frac{78}{161}\right)$	$e\left(\frac{416}{483}\right)$	$e\left(\frac{31}{161}\right)$	$e\left(\frac{431}{483}\right)$
$\chi_{4031}(21,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{515}{1932}\right)$	$e\left(\frac{139}{1932}\right)$	$e\left(\frac{515}{966}\right)$	$e\left(\frac{65}{966}\right)$	$e\left(\frac{109}{322}\right)$	$e\left(\frac{124}{483}\right)$	$e\left(\frac{515}{644}\right)$	$e\left(\frac{139}{966}\right)$	$e\left(\frac{215}{644}\right)$	$e\left(\frac{569}{1932}\right)$
$\chi_{4031}(22,\cdot)$	4031.br	966	yes	$-1$	$1$	$e\left(\frac{235}{483}\right)$	$e\left(\frac{251}{483}\right)$	$e\left(\frac{470}{483}\right)$	$e\left(\frac{200}{483}\right)$	$e\left(\frac{1}{161}\right)$	$e\left(\frac{20}{483}\right)$	$e\left(\frac{74}{161}\right)$	$e\left(\frac{19}{483}\right)$	$e\left(\frac{145}{161}\right)$	$e\left(\frac{599}{966}\right)$
$\chi_{4031}(23,\cdot)$	4031.bm	322	yes	$-1$	$1$	$e\left(\frac{293}{322}\right)$	$e\left(\frac{191}{322}\right)$	$e\left(\frac{132}{161}\right)$	$e\left(\frac{87}{161}\right)$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{57}{161}\right)$	$e\left(\frac{235}{322}\right)$	$e\left(\frac{30}{161}\right)$	$e\left(\frac{145}{322}\right)$	$e\left(\frac{117}{161}\right)$
$\chi_{4031}(24,\cdot)$	4031.bo	483	yes	$1$	$1$	$e\left(\frac{292}{483}\right)$	$e\left(\frac{242}{483}\right)$	$e\left(\frac{101}{483}\right)$	$e\left(\frac{341}{483}\right)$	$e\left(\frac{17}{161}\right)$	$e\left(\frac{179}{483}\right)$	$e\left(\frac{131}{161}\right)$	$e\left(\frac{1}{483}\right)$	$e\left(\frac{50}{161}\right)$	$e\left(\frac{181}{483}\right)$
$\chi_{4031}(25,\cdot)$	4031.bo	483	yes	$1$	$1$	$e\left(\frac{395}{483}\right)$	$e\left(\frac{463}{483}\right)$	$e\left(\frac{307}{483}\right)$	$e\left(\frac{367}{483}\right)$	$e\left(\frac{125}{161}\right)$	$e\left(\frac{85}{483}\right)$	$e\left(\frac{73}{161}\right)$	$e\left(\frac{443}{483}\right)$	$e\left(\frac{93}{161}\right)$	$e\left(\frac{5}{483}\right)$
$\chi_{4031}(26,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{289}{1932}\right)$	$e\left(\frac{1361}{1932}\right)$	$e\left(\frac{289}{966}\right)$	$e\left(\frac{421}{966}\right)$	$e\left(\frac{275}{322}\right)$	$e\left(\frac{335}{483}\right)$	$e\left(\frac{289}{644}\right)$	$e\left(\frac{395}{966}\right)$	$e\left(\frac{377}{644}\right)$	$e\left(\frac{1471}{1932}\right)$
$\chi_{4031}(27,\cdot)$	4031.bq	644	yes	$1$	$1$	$e\left(\frac{275}{644}\right)$	$e\left(\frac{143}{644}\right)$	$e\left(\frac{275}{322}\right)$	$e\left(\frac{141}{322}\right)$	$e\left(\frac{209}{322}\right)$	$e\left(\frac{160}{161}\right)$	$e\left(\frac{181}{644}\right)$	$e\left(\frac{143}{322}\right)$	$e\left(\frac{557}{644}\right)$	$e\left(\frac{85}{644}\right)$
$\chi_{4031}(28,\cdot)$	4031.bf	138	yes	$1$	$1$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{58}{69}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{19}{138}\right)$
$\chi_{4031}(30,\cdot)$	4031.ba	69	no	$1$	$1$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{2}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{34}{69}\right)$
$\chi_{4031}(31,\cdot)$	4031.bv	1932	yes	$-1$	$1$	$e\left(\frac{853}{1932}\right)$	$e\left(\frac{1577}{1932}\right)$	$e\left(\frac{853}{966}\right)$	$e\left(\frac{661}{966}\right)$	$e\left(\frac{83}{322}\right)$	$e\left(\frac{347}{483}\right)$	$e\left(\frac{209}{644}\right)$	$e\left(\frac{611}{966}\right)$	$e\left(\frac{81}{644}\right)$	$e\left(\frac{1417}{1932}\right)$
$\chi_{4031}(32,\cdot)$	4031.bu	1932	yes	$1$	$1$	$e\left(\frac{415}{1932}\right)$	$e\left(\frac{731}{1932}\right)$	$e\left(\frac{415}{966}\right)$	$e\left(\frac{43}{966}\right)$	$e\left(\frac{191}{322}\right)$	$e\left(\frac{461}{483}\right)$	$e\left(\frac{415}{644}\right)$	$e\left(\frac{731}{966}\right)$	$e\left(\frac{167}{644}\right)$	$e\left(\frac{421}{1932}\right)$
$\chi_{4031}(33,\cdot)$	4031.bn	322	yes	$-1$	$1$	$e\left(\frac{148}{161}\right)$	$e\left(\frac{19}{161}\right)$	$e\left(\frac{135}{161}\right)$	$e\left(\frac{78}{161}\right)$	$e\left(\frac{6}{161}\right)$	$e\left(\frac{40}{161}\right)$	$e\left(\frac{122}{161}\right)$	$e\left(\frac{38}{161}\right)$	$e\left(\frac{65}{161}\right)$	$e\left(\frac{71}{322}\right)$

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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	$4031$
Structure	\(C_{2}\times C_{1932}\)
Order	$3864$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4031}(1,\cdot)\)	4031.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4031}(2,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{83}{1932}\right)\)	\(e\left(\frac{919}{1932}\right)\)	\(e\left(\frac{83}{966}\right)\)	\(e\left(\frac{395}{966}\right)\)	\(e\left(\frac{167}{322}\right)\)	\(e\left(\frac{382}{483}\right)\)	\(e\left(\frac{83}{644}\right)\)	\(e\left(\frac{919}{966}\right)\)	\(e\left(\frac{291}{644}\right)\)	\(e\left(\frac{857}{1932}\right)\)
\(\chi_{4031}(3,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{919}{1932}\right)\)	\(e\left(\frac{143}{1932}\right)\)	\(e\left(\frac{919}{966}\right)\)	\(e\left(\frac{463}{966}\right)\)	\(e\left(\frac{177}{322}\right)\)	\(e\left(\frac{482}{483}\right)\)	\(e\left(\frac{275}{644}\right)\)	\(e\left(\frac{143}{966}\right)\)	\(e\left(\frac{615}{644}\right)\)	\(e\left(\frac{85}{1932}\right)\)
\(\chi_{4031}(4,\cdot)\)	4031.bt	966	yes	\(1\)	\(1\)	\(e\left(\frac{83}{966}\right)\)	\(e\left(\frac{919}{966}\right)\)	\(e\left(\frac{83}{483}\right)\)	\(e\left(\frac{395}{483}\right)\)	\(e\left(\frac{6}{161}\right)\)	\(e\left(\frac{281}{483}\right)\)	\(e\left(\frac{83}{322}\right)\)	\(e\left(\frac{436}{483}\right)\)	\(e\left(\frac{291}{322}\right)\)	\(e\left(\frac{857}{966}\right)\)
\(\chi_{4031}(5,\cdot)\)	4031.bt	966	yes	\(1\)	\(1\)	\(e\left(\frac{395}{966}\right)\)	\(e\left(\frac{463}{966}\right)\)	\(e\left(\frac{395}{483}\right)\)	\(e\left(\frac{425}{483}\right)\)	\(e\left(\frac{143}{161}\right)\)	\(e\left(\frac{284}{483}\right)\)	\(e\left(\frac{73}{322}\right)\)	\(e\left(\frac{463}{483}\right)\)	\(e\left(\frac{93}{322}\right)\)	\(e\left(\frac{5}{966}\right)\)
\(\chi_{4031}(6,\cdot)\)	4031.bl	322	yes	\(1\)	\(1\)	\(e\left(\frac{167}{322}\right)\)	\(e\left(\frac{177}{322}\right)\)	\(e\left(\frac{6}{161}\right)\)	\(e\left(\frac{143}{161}\right)\)	\(e\left(\frac{11}{161}\right)\)	\(e\left(\frac{127}{161}\right)\)	\(e\left(\frac{179}{322}\right)\)	\(e\left(\frac{16}{161}\right)\)	\(e\left(\frac{131}{322}\right)\)	\(e\left(\frac{157}{322}\right)\)
\(\chi_{4031}(7,\cdot)\)	4031.bo	483	yes	\(1\)	\(1\)	\(e\left(\frac{382}{483}\right)\)	\(e\left(\frac{482}{483}\right)\)	\(e\left(\frac{281}{483}\right)\)	\(e\left(\frac{284}{483}\right)\)	\(e\left(\frac{127}{161}\right)\)	\(e\left(\frac{125}{483}\right)\)	\(e\left(\frac{60}{161}\right)\)	\(e\left(\frac{481}{483}\right)\)	\(e\left(\frac{61}{161}\right)\)	\(e\left(\frac{121}{483}\right)\)
\(\chi_{4031}(8,\cdot)\)	4031.bq	644	yes	\(1\)	\(1\)	\(e\left(\frac{83}{644}\right)\)	\(e\left(\frac{275}{644}\right)\)	\(e\left(\frac{83}{322}\right)\)	\(e\left(\frac{73}{322}\right)\)	\(e\left(\frac{179}{322}\right)\)	\(e\left(\frac{60}{161}\right)\)	\(e\left(\frac{249}{644}\right)\)	\(e\left(\frac{275}{322}\right)\)	\(e\left(\frac{229}{644}\right)\)	\(e\left(\frac{213}{644}\right)\)
\(\chi_{4031}(9,\cdot)\)	4031.bt	966	yes	\(1\)	\(1\)	\(e\left(\frac{919}{966}\right)\)	\(e\left(\frac{143}{966}\right)\)	\(e\left(\frac{436}{483}\right)\)	\(e\left(\frac{463}{483}\right)\)	\(e\left(\frac{16}{161}\right)\)	\(e\left(\frac{481}{483}\right)\)	\(e\left(\frac{275}{322}\right)\)	\(e\left(\frac{143}{483}\right)\)	\(e\left(\frac{293}{322}\right)\)	\(e\left(\frac{85}{966}\right)\)
\(\chi_{4031}(10,\cdot)\)	4031.bq	644	yes	\(1\)	\(1\)	\(e\left(\frac{291}{644}\right)\)	\(e\left(\frac{615}{644}\right)\)	\(e\left(\frac{291}{322}\right)\)	\(e\left(\frac{93}{322}\right)\)	\(e\left(\frac{131}{322}\right)\)	\(e\left(\frac{61}{161}\right)\)	\(e\left(\frac{229}{644}\right)\)	\(e\left(\frac{293}{322}\right)\)	\(e\left(\frac{477}{644}\right)\)	\(e\left(\frac{289}{644}\right)\)
\(\chi_{4031}(11,\cdot)\)	4031.bv	1932	yes	\(-1\)	\(1\)	\(e\left(\frac{857}{1932}\right)\)	\(e\left(\frac{85}{1932}\right)\)	\(e\left(\frac{857}{966}\right)\)	\(e\left(\frac{5}{966}\right)\)	\(e\left(\frac{157}{322}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{213}{644}\right)\)	\(e\left(\frac{85}{966}\right)\)	\(e\left(\frac{289}{644}\right)\)	\(e\left(\frac{341}{1932}\right)\)
\(\chi_{4031}(12,\cdot)\)	4031.bk	276	yes	\(1\)	\(1\)	\(e\left(\frac{155}{276}\right)\)	\(e\left(\frac{7}{276}\right)\)	\(e\left(\frac{17}{138}\right)\)	\(e\left(\frac{41}{138}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{257}{276}\right)\)
\(\chi_{4031}(13,\cdot)\)	4031.bt	966	yes	\(1\)	\(1\)	\(e\left(\frac{103}{966}\right)\)	\(e\left(\frac{221}{966}\right)\)	\(e\left(\frac{103}{483}\right)\)	\(e\left(\frac{13}{483}\right)\)	\(e\left(\frac{54}{161}\right)\)	\(e\left(\frac{436}{483}\right)\)	\(e\left(\frac{103}{322}\right)\)	\(e\left(\frac{221}{483}\right)\)	\(e\left(\frac{43}{322}\right)\)	\(e\left(\frac{307}{966}\right)\)
\(\chi_{4031}(14,\cdot)\)	4031.bq	644	yes	\(1\)	\(1\)	\(e\left(\frac{537}{644}\right)\)	\(e\left(\frac{305}{644}\right)\)	\(e\left(\frac{215}{322}\right)\)	\(e\left(\frac{321}{322}\right)\)	\(e\left(\frac{99}{322}\right)\)	\(e\left(\frac{8}{161}\right)\)	\(e\left(\frac{323}{644}\right)\)	\(e\left(\frac{305}{322}\right)\)	\(e\left(\frac{535}{644}\right)\)	\(e\left(\frac{447}{644}\right)\)
\(\chi_{4031}(15,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{1709}{1932}\right)\)	\(e\left(\frac{1069}{1932}\right)\)	\(e\left(\frac{743}{966}\right)\)	\(e\left(\frac{347}{966}\right)\)	\(e\left(\frac{141}{322}\right)\)	\(e\left(\frac{283}{483}\right)\)	\(e\left(\frac{421}{644}\right)\)	\(e\left(\frac{103}{966}\right)\)	\(e\left(\frac{157}{644}\right)\)	\(e\left(\frac{95}{1932}\right)\)
\(\chi_{4031}(16,\cdot)\)	4031.bo	483	yes	\(1\)	\(1\)	\(e\left(\frac{83}{483}\right)\)	\(e\left(\frac{436}{483}\right)\)	\(e\left(\frac{166}{483}\right)\)	\(e\left(\frac{307}{483}\right)\)	\(e\left(\frac{12}{161}\right)\)	\(e\left(\frac{79}{483}\right)\)	\(e\left(\frac{83}{161}\right)\)	\(e\left(\frac{389}{483}\right)\)	\(e\left(\frac{130}{161}\right)\)	\(e\left(\frac{374}{483}\right)\)
\(\chi_{4031}(17,\cdot)\)	4031.bk	276	yes	\(1\)	\(1\)	\(e\left(\frac{145}{276}\right)\)	\(e\left(\frac{149}{276}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{11}{138}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{187}{276}\right)\)
\(\chi_{4031}(18,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{1921}{1932}\right)\)	\(e\left(\frac{1205}{1932}\right)\)	\(e\left(\frac{955}{966}\right)\)	\(e\left(\frac{355}{966}\right)\)	\(e\left(\frac{199}{322}\right)\)	\(e\left(\frac{380}{483}\right)\)	\(e\left(\frac{633}{644}\right)\)	\(e\left(\frac{239}{966}\right)\)	\(e\left(\frac{233}{644}\right)\)	\(e\left(\frac{1027}{1932}\right)\)
\(\chi_{4031}(19,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{1475}{1932}\right)\)	\(e\left(\frac{1411}{1932}\right)\)	\(e\left(\frac{509}{966}\right)\)	\(e\left(\frac{83}{966}\right)\)	\(e\left(\frac{159}{322}\right)\)	\(e\left(\frac{463}{483}\right)\)	\(e\left(\frac{187}{644}\right)\)	\(e\left(\frac{445}{966}\right)\)	\(e\left(\frac{547}{644}\right)\)	\(e\left(\frac{1217}{1932}\right)\)
\(\chi_{4031}(20,\cdot)\)	4031.bo	483	yes	\(1\)	\(1\)	\(e\left(\frac{239}{483}\right)\)	\(e\left(\frac{208}{483}\right)\)	\(e\left(\frac{478}{483}\right)\)	\(e\left(\frac{337}{483}\right)\)	\(e\left(\frac{149}{161}\right)\)	\(e\left(\frac{82}{483}\right)\)	\(e\left(\frac{78}{161}\right)\)	\(e\left(\frac{416}{483}\right)\)	\(e\left(\frac{31}{161}\right)\)	\(e\left(\frac{431}{483}\right)\)
\(\chi_{4031}(21,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{515}{1932}\right)\)	\(e\left(\frac{139}{1932}\right)\)	\(e\left(\frac{515}{966}\right)\)	\(e\left(\frac{65}{966}\right)\)	\(e\left(\frac{109}{322}\right)\)	\(e\left(\frac{124}{483}\right)\)	\(e\left(\frac{515}{644}\right)\)	\(e\left(\frac{139}{966}\right)\)	\(e\left(\frac{215}{644}\right)\)	\(e\left(\frac{569}{1932}\right)\)
\(\chi_{4031}(22,\cdot)\)	4031.br	966	yes	\(-1\)	\(1\)	\(e\left(\frac{235}{483}\right)\)	\(e\left(\frac{251}{483}\right)\)	\(e\left(\frac{470}{483}\right)\)	\(e\left(\frac{200}{483}\right)\)	\(e\left(\frac{1}{161}\right)\)	\(e\left(\frac{20}{483}\right)\)	\(e\left(\frac{74}{161}\right)\)	\(e\left(\frac{19}{483}\right)\)	\(e\left(\frac{145}{161}\right)\)	\(e\left(\frac{599}{966}\right)\)
\(\chi_{4031}(23,\cdot)\)	4031.bm	322	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{322}\right)\)	\(e\left(\frac{191}{322}\right)\)	\(e\left(\frac{132}{161}\right)\)	\(e\left(\frac{87}{161}\right)\)	\(e\left(\frac{81}{161}\right)\)	\(e\left(\frac{57}{161}\right)\)	\(e\left(\frac{235}{322}\right)\)	\(e\left(\frac{30}{161}\right)\)	\(e\left(\frac{145}{322}\right)\)	\(e\left(\frac{117}{161}\right)\)
\(\chi_{4031}(24,\cdot)\)	4031.bo	483	yes	\(1\)	\(1\)	\(e\left(\frac{292}{483}\right)\)	\(e\left(\frac{242}{483}\right)\)	\(e\left(\frac{101}{483}\right)\)	\(e\left(\frac{341}{483}\right)\)	\(e\left(\frac{17}{161}\right)\)	\(e\left(\frac{179}{483}\right)\)	\(e\left(\frac{131}{161}\right)\)	\(e\left(\frac{1}{483}\right)\)	\(e\left(\frac{50}{161}\right)\)	\(e\left(\frac{181}{483}\right)\)
\(\chi_{4031}(25,\cdot)\)	4031.bo	483	yes	\(1\)	\(1\)	\(e\left(\frac{395}{483}\right)\)	\(e\left(\frac{463}{483}\right)\)	\(e\left(\frac{307}{483}\right)\)	\(e\left(\frac{367}{483}\right)\)	\(e\left(\frac{125}{161}\right)\)	\(e\left(\frac{85}{483}\right)\)	\(e\left(\frac{73}{161}\right)\)	\(e\left(\frac{443}{483}\right)\)	\(e\left(\frac{93}{161}\right)\)	\(e\left(\frac{5}{483}\right)\)
\(\chi_{4031}(26,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{289}{1932}\right)\)	\(e\left(\frac{1361}{1932}\right)\)	\(e\left(\frac{289}{966}\right)\)	\(e\left(\frac{421}{966}\right)\)	\(e\left(\frac{275}{322}\right)\)	\(e\left(\frac{335}{483}\right)\)	\(e\left(\frac{289}{644}\right)\)	\(e\left(\frac{395}{966}\right)\)	\(e\left(\frac{377}{644}\right)\)	\(e\left(\frac{1471}{1932}\right)\)
\(\chi_{4031}(27,\cdot)\)	4031.bq	644	yes	\(1\)	\(1\)	\(e\left(\frac{275}{644}\right)\)	\(e\left(\frac{143}{644}\right)\)	\(e\left(\frac{275}{322}\right)\)	\(e\left(\frac{141}{322}\right)\)	\(e\left(\frac{209}{322}\right)\)	\(e\left(\frac{160}{161}\right)\)	\(e\left(\frac{181}{644}\right)\)	\(e\left(\frac{143}{322}\right)\)	\(e\left(\frac{557}{644}\right)\)	\(e\left(\frac{85}{644}\right)\)
\(\chi_{4031}(28,\cdot)\)	4031.bf	138	yes	\(1\)	\(1\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{58}{69}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{19}{138}\right)\)
\(\chi_{4031}(30,\cdot)\)	4031.ba	69	no	\(1\)	\(1\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{2}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{34}{69}\right)\)
\(\chi_{4031}(31,\cdot)\)	4031.bv	1932	yes	\(-1\)	\(1\)	\(e\left(\frac{853}{1932}\right)\)	\(e\left(\frac{1577}{1932}\right)\)	\(e\left(\frac{853}{966}\right)\)	\(e\left(\frac{661}{966}\right)\)	\(e\left(\frac{83}{322}\right)\)	\(e\left(\frac{347}{483}\right)\)	\(e\left(\frac{209}{644}\right)\)	\(e\left(\frac{611}{966}\right)\)	\(e\left(\frac{81}{644}\right)\)	\(e\left(\frac{1417}{1932}\right)\)
\(\chi_{4031}(32,\cdot)\)	4031.bu	1932	yes	\(1\)	\(1\)	\(e\left(\frac{415}{1932}\right)\)	\(e\left(\frac{731}{1932}\right)\)	\(e\left(\frac{415}{966}\right)\)	\(e\left(\frac{43}{966}\right)\)	\(e\left(\frac{191}{322}\right)\)	\(e\left(\frac{461}{483}\right)\)	\(e\left(\frac{415}{644}\right)\)	\(e\left(\frac{731}{966}\right)\)	\(e\left(\frac{167}{644}\right)\)	\(e\left(\frac{421}{1932}\right)\)
\(\chi_{4031}(33,\cdot)\)	4031.bn	322	yes	\(-1\)	\(1\)	\(e\left(\frac{148}{161}\right)\)	\(e\left(\frac{19}{161}\right)\)	\(e\left(\frac{135}{161}\right)\)	\(e\left(\frac{78}{161}\right)\)	\(e\left(\frac{6}{161}\right)\)	\(e\left(\frac{40}{161}\right)\)	\(e\left(\frac{122}{161}\right)\)	\(e\left(\frac{38}{161}\right)\)	\(e\left(\frac{65}{161}\right)\)	\(e\left(\frac{71}{322}\right)\)

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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.