LMFDB - Group of Dirichlet Characters of Modulus 1031

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(1031)

pari: g = idealstar(,1031,2)

Character group

sage: G.order() pari: g.no
Order	=	1030
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1030}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1031}(14,\cdot)$

First 32 of 1030 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.

	orbit label	order	primitive	-1	1	2	3	4	5	6	7	8	9	10	11
$\chi_{1031}(1,\cdot)$	1031.a	1	No	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1031}(2,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{83}{515}\right)$	$e\left(\frac{168}{515}\right)$	$e\left(\frac{166}{515}\right)$	$e\left(\frac{392}{515}\right)$	$e\left(\frac{251}{515}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{249}{515}\right)$	$e\left(\frac{336}{515}\right)$	$e\left(\frac{95}{103}\right)$	$e\left(\frac{201}{515}\right)$
$\chi_{1031}(3,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{168}{515}\right)$	$e\left(\frac{278}{515}\right)$	$e\left(\frac{336}{515}\right)$	$e\left(\frac{477}{515}\right)$	$e\left(\frac{446}{515}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{504}{515}\right)$	$e\left(\frac{41}{515}\right)$	$e\left(\frac{26}{103}\right)$	$e\left(\frac{351}{515}\right)$
$\chi_{1031}(4,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{166}{515}\right)$	$e\left(\frac{336}{515}\right)$	$e\left(\frac{332}{515}\right)$	$e\left(\frac{269}{515}\right)$	$e\left(\frac{502}{515}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{498}{515}\right)$	$e\left(\frac{157}{515}\right)$	$e\left(\frac{87}{103}\right)$	$e\left(\frac{402}{515}\right)$
$\chi_{1031}(5,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{392}{515}\right)$	$e\left(\frac{477}{515}\right)$	$e\left(\frac{269}{515}\right)$	$e\left(\frac{83}{515}\right)$	$e\left(\frac{354}{515}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{146}{515}\right)$	$e\left(\frac{439}{515}\right)$	$e\left(\frac{95}{103}\right)$	$e\left(\frac{304}{515}\right)$
$\chi_{1031}(6,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{251}{515}\right)$	$e\left(\frac{446}{515}\right)$	$e\left(\frac{502}{515}\right)$	$e\left(\frac{354}{515}\right)$	$e\left(\frac{182}{515}\right)$	$e\left(\frac{90}{103}\right)$	$e\left(\frac{238}{515}\right)$	$e\left(\frac{377}{515}\right)$	$e\left(\frac{18}{103}\right)$	$e\left(\frac{37}{515}\right)$
$\chi_{1031}(7,\cdot)$	1031.f	206	Yes	$-1$	$1$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{90}{103}\right)$	$e\left(\frac{127}{206}\right)$	$e\left(\frac{86}{103}\right)$	$e\left(\frac{54}{103}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{93}{103}\right)$
$\chi_{1031}(8,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{249}{515}\right)$	$e\left(\frac{504}{515}\right)$	$e\left(\frac{498}{515}\right)$	$e\left(\frac{146}{515}\right)$	$e\left(\frac{238}{515}\right)$	$e\left(\frac{86}{103}\right)$	$e\left(\frac{232}{515}\right)$	$e\left(\frac{493}{515}\right)$	$e\left(\frac{79}{103}\right)$	$e\left(\frac{88}{515}\right)$
$\chi_{1031}(9,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{336}{515}\right)$	$e\left(\frac{41}{515}\right)$	$e\left(\frac{157}{515}\right)$	$e\left(\frac{439}{515}\right)$	$e\left(\frac{377}{515}\right)$	$e\left(\frac{54}{103}\right)$	$e\left(\frac{493}{515}\right)$	$e\left(\frac{82}{515}\right)$	$e\left(\frac{52}{103}\right)$	$e\left(\frac{187}{515}\right)$
$\chi_{1031}(10,\cdot)$	1031.e	103	Yes	$1$	$1$	$e\left(\frac{95}{103}\right)$	$e\left(\frac{26}{103}\right)$	$e\left(\frac{87}{103}\right)$	$e\left(\frac{95}{103}\right)$	$e\left(\frac{18}{103}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{79}{103}\right)$	$e\left(\frac{52}{103}\right)$	$e\left(\frac{87}{103}\right)$	$e\left(\frac{101}{103}\right)$
$\chi_{1031}(11,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{201}{515}\right)$	$e\left(\frac{351}{515}\right)$	$e\left(\frac{402}{515}\right)$	$e\left(\frac{304}{515}\right)$	$e\left(\frac{37}{515}\right)$	$e\left(\frac{93}{103}\right)$	$e\left(\frac{88}{515}\right)$	$e\left(\frac{187}{515}\right)$	$e\left(\frac{101}{103}\right)$	$e\left(\frac{282}{515}\right)$
$\chi_{1031}(12,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{334}{515}\right)$	$e\left(\frac{99}{515}\right)$	$e\left(\frac{153}{515}\right)$	$e\left(\frac{231}{515}\right)$	$e\left(\frac{433}{515}\right)$	$e\left(\frac{50}{103}\right)$	$e\left(\frac{487}{515}\right)$	$e\left(\frac{198}{515}\right)$	$e\left(\frac{10}{103}\right)$	$e\left(\frac{238}{515}\right)$
$\chi_{1031}(13,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{127}{515}\right)$	$e\left(\frac{437}{515}\right)$	$e\left(\frac{254}{515}\right)$	$e\left(\frac{333}{515}\right)$	$e\left(\frac{49}{515}\right)$	$e\left(\frac{48}{103}\right)$	$e\left(\frac{381}{515}\right)$	$e\left(\frac{359}{515}\right)$	$e\left(\frac{92}{103}\right)$	$e\left(\frac{109}{515}\right)$
$\chi_{1031}(14,\cdot)$	1031.h	1030	Yes	$-1$	$1$	$e\left(\frac{398}{515}\right)$	$e\left(\frac{303}{515}\right)$	$e\left(\frac{281}{515}\right)$	$e\left(\frac{192}{515}\right)$	$e\left(\frac{186}{515}\right)$	$e\left(\frac{47}{206}\right)$	$e\left(\frac{164}{515}\right)$	$e\left(\frac{91}{515}\right)$	$e\left(\frac{15}{103}\right)$	$e\left(\frac{151}{515}\right)$
$\chi_{1031}(15,\cdot)$	1031.e	103	Yes	$1$	$1$	$e\left(\frac{9}{103}\right)$	$e\left(\frac{48}{103}\right)$	$e\left(\frac{18}{103}\right)$	$e\left(\frac{9}{103}\right)$	$e\left(\frac{57}{103}\right)$	$e\left(\frac{90}{103}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{96}{103}\right)$	$e\left(\frac{18}{103}\right)$	$e\left(\frac{28}{103}\right)$
$\chi_{1031}(16,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{332}{515}\right)$	$e\left(\frac{157}{515}\right)$	$e\left(\frac{149}{515}\right)$	$e\left(\frac{23}{515}\right)$	$e\left(\frac{489}{515}\right)$	$e\left(\frac{46}{103}\right)$	$e\left(\frac{481}{515}\right)$	$e\left(\frac{314}{515}\right)$	$e\left(\frac{71}{103}\right)$	$e\left(\frac{289}{515}\right)$
$\chi_{1031}(17,\cdot)$	1031.f	206	Yes	$-1$	$1$	$e\left(\frac{101}{103}\right)$	$e\left(\frac{58}{103}\right)$	$e\left(\frac{99}{103}\right)$	$e\left(\frac{101}{103}\right)$	$e\left(\frac{56}{103}\right)$	$e\left(\frac{63}{206}\right)$	$e\left(\frac{97}{103}\right)$	$e\left(\frac{13}{103}\right)$	$e\left(\frac{99}{103}\right)$	$e\left(\frac{51}{103}\right)$
$\chi_{1031}(18,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{419}{515}\right)$	$e\left(\frac{209}{515}\right)$	$e\left(\frac{323}{515}\right)$	$e\left(\frac{316}{515}\right)$	$e\left(\frac{113}{515}\right)$	$e\left(\frac{14}{103}\right)$	$e\left(\frac{227}{515}\right)$	$e\left(\frac{418}{515}\right)$	$e\left(\frac{44}{103}\right)$	$e\left(\frac{388}{515}\right)$
$\chi_{1031}(19,\cdot)$	1031.f	206	Yes	$-1$	$1$	$e\left(\frac{64}{103}\right)$	$e\left(\frac{101}{103}\right)$	$e\left(\frac{25}{103}\right)$	$e\left(\frac{64}{103}\right)$	$e\left(\frac{62}{103}\right)$	$e\left(\frac{147}{206}\right)$	$e\left(\frac{89}{103}\right)$	$e\left(\frac{99}{103}\right)$	$e\left(\frac{25}{103}\right)$	$e\left(\frac{16}{103}\right)$
$\chi_{1031}(20,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{43}{515}\right)$	$e\left(\frac{298}{515}\right)$	$e\left(\frac{86}{515}\right)$	$e\left(\frac{352}{515}\right)$	$e\left(\frac{341}{515}\right)$	$e\left(\frac{86}{103}\right)$	$e\left(\frac{129}{515}\right)$	$e\left(\frac{81}{515}\right)$	$e\left(\frac{79}{103}\right)$	$e\left(\frac{191}{515}\right)$
$\chi_{1031}(21,\cdot)$	1031.h	1030	Yes	$-1$	$1$	$e\left(\frac{483}{515}\right)$	$e\left(\frac{413}{515}\right)$	$e\left(\frac{451}{515}\right)$	$e\left(\frac{277}{515}\right)$	$e\left(\frac{381}{515}\right)$	$e\left(\frac{181}{206}\right)$	$e\left(\frac{419}{515}\right)$	$e\left(\frac{311}{515}\right)$	$e\left(\frac{49}{103}\right)$	$e\left(\frac{301}{515}\right)$
$\chi_{1031}(22,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{284}{515}\right)$	$e\left(\frac{4}{515}\right)$	$e\left(\frac{53}{515}\right)$	$e\left(\frac{181}{515}\right)$	$e\left(\frac{288}{515}\right)$	$e\left(\frac{53}{103}\right)$	$e\left(\frac{337}{515}\right)$	$e\left(\frac{8}{515}\right)$	$e\left(\frac{93}{103}\right)$	$e\left(\frac{483}{515}\right)$
$\chi_{1031}(23,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{468}{515}\right)$	$e\left(\frac{333}{515}\right)$	$e\left(\frac{421}{515}\right)$	$e\left(\frac{262}{515}\right)$	$e\left(\frac{286}{515}\right)$	$e\left(\frac{9}{103}\right)$	$e\left(\frac{374}{515}\right)$	$e\left(\frac{151}{515}\right)$	$e\left(\frac{43}{103}\right)$	$e\left(\frac{426}{515}\right)$
$\chi_{1031}(24,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{417}{515}\right)$	$e\left(\frac{267}{515}\right)$	$e\left(\frac{319}{515}\right)$	$e\left(\frac{108}{515}\right)$	$e\left(\frac{169}{515}\right)$	$e\left(\frac{10}{103}\right)$	$e\left(\frac{221}{515}\right)$	$e\left(\frac{19}{515}\right)$	$e\left(\frac{2}{103}\right)$	$e\left(\frac{439}{515}\right)$
$\chi_{1031}(25,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{269}{515}\right)$	$e\left(\frac{439}{515}\right)$	$e\left(\frac{23}{515}\right)$	$e\left(\frac{166}{515}\right)$	$e\left(\frac{193}{515}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{292}{515}\right)$	$e\left(\frac{363}{515}\right)$	$e\left(\frac{87}{103}\right)$	$e\left(\frac{93}{515}\right)$
$\chi_{1031}(26,\cdot)$	1031.e	103	Yes	$1$	$1$	$e\left(\frac{42}{103}\right)$	$e\left(\frac{18}{103}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{42}{103}\right)$	$e\left(\frac{60}{103}\right)$	$e\left(\frac{8}{103}\right)$	$e\left(\frac{23}{103}\right)$	$e\left(\frac{36}{103}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{62}{103}\right)$
$\chi_{1031}(27,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{504}{515}\right)$	$e\left(\frac{319}{515}\right)$	$e\left(\frac{493}{515}\right)$	$e\left(\frac{401}{515}\right)$	$e\left(\frac{308}{515}\right)$	$e\left(\frac{81}{103}\right)$	$e\left(\frac{482}{515}\right)$	$e\left(\frac{123}{515}\right)$	$e\left(\frac{78}{103}\right)$	$e\left(\frac{23}{515}\right)$
$\chi_{1031}(28,\cdot)$	1031.h	1030	Yes	$-1$	$1$	$e\left(\frac{481}{515}\right)$	$e\left(\frac{471}{515}\right)$	$e\left(\frac{447}{515}\right)$	$e\left(\frac{69}{515}\right)$	$e\left(\frac{437}{515}\right)$	$e\left(\frac{173}{206}\right)$	$e\left(\frac{413}{515}\right)$	$e\left(\frac{427}{515}\right)$	$e\left(\frac{7}{103}\right)$	$e\left(\frac{352}{515}\right)$
$\chi_{1031}(29,\cdot)$	1031.e	103	Yes	$1$	$1$	$e\left(\frac{28}{103}\right)$	$e\left(\frac{12}{103}\right)$	$e\left(\frac{56}{103}\right)$	$e\left(\frac{28}{103}\right)$	$e\left(\frac{40}{103}\right)$	$e\left(\frac{74}{103}\right)$	$e\left(\frac{84}{103}\right)$	$e\left(\frac{24}{103}\right)$	$e\left(\frac{56}{103}\right)$	$e\left(\frac{7}{103}\right)$
$\chi_{1031}(30,\cdot)$	1031.g	515	Yes	$1$	$1$	$e\left(\frac{128}{515}\right)$	$e\left(\frac{408}{515}\right)$	$e\left(\frac{256}{515}\right)$	$e\left(\frac{437}{515}\right)$	$e\left(\frac{21}{515}\right)$	$e\left(\frac{50}{103}\right)$	$e\left(\frac{384}{515}\right)$	$e\left(\frac{301}{515}\right)$	$e\left(\frac{10}{103}\right)$	$e\left(\frac{341}{515}\right)$
$\chi_{1031}(31,\cdot)$	1031.f	206	Yes	$-1$	$1$	$e\left(\frac{79}{103}\right)$	$e\left(\frac{78}{103}\right)$	$e\left(\frac{55}{103}\right)$	$e\left(\frac{79}{103}\right)$	$e\left(\frac{54}{103}\right)$	$e\left(\frac{35}{206}\right)$	$e\left(\frac{31}{103}\right)$	$e\left(\frac{53}{103}\right)$	$e\left(\frac{55}{103}\right)$	$e\left(\frac{97}{103}\right)$
$\chi_{1031}(32,\cdot)$	1031.e	103	Yes	$1$	$1$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{65}{103}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{83}{103}\right)$	$e\left(\frac{45}{103}\right)$	$e\left(\frac{6}{103}\right)$	$e\left(\frac{43}{103}\right)$	$e\left(\frac{27}{103}\right)$	$e\left(\frac{63}{103}\right)$	$e\left(\frac{98}{103}\right)$

Introduction	Features
Universe	News

	orbit label	order	primitive	-1	1	2	3	4	5	6	7	8	9	10	11
\(\chi_{1031}(1,\cdot)\)	1031.a	1	No	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1031}(2,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{83}{515}\right)\)	\(e\left(\frac{168}{515}\right)\)	\(e\left(\frac{166}{515}\right)\)	\(e\left(\frac{392}{515}\right)\)	\(e\left(\frac{251}{515}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{249}{515}\right)\)	\(e\left(\frac{336}{515}\right)\)	\(e\left(\frac{95}{103}\right)\)	\(e\left(\frac{201}{515}\right)\)
\(\chi_{1031}(3,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{168}{515}\right)\)	\(e\left(\frac{278}{515}\right)\)	\(e\left(\frac{336}{515}\right)\)	\(e\left(\frac{477}{515}\right)\)	\(e\left(\frac{446}{515}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{504}{515}\right)\)	\(e\left(\frac{41}{515}\right)\)	\(e\left(\frac{26}{103}\right)\)	\(e\left(\frac{351}{515}\right)\)
\(\chi_{1031}(4,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{166}{515}\right)\)	\(e\left(\frac{336}{515}\right)\)	\(e\left(\frac{332}{515}\right)\)	\(e\left(\frac{269}{515}\right)\)	\(e\left(\frac{502}{515}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{498}{515}\right)\)	\(e\left(\frac{157}{515}\right)\)	\(e\left(\frac{87}{103}\right)\)	\(e\left(\frac{402}{515}\right)\)
\(\chi_{1031}(5,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{392}{515}\right)\)	\(e\left(\frac{477}{515}\right)\)	\(e\left(\frac{269}{515}\right)\)	\(e\left(\frac{83}{515}\right)\)	\(e\left(\frac{354}{515}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{146}{515}\right)\)	\(e\left(\frac{439}{515}\right)\)	\(e\left(\frac{95}{103}\right)\)	\(e\left(\frac{304}{515}\right)\)
\(\chi_{1031}(6,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{251}{515}\right)\)	\(e\left(\frac{446}{515}\right)\)	\(e\left(\frac{502}{515}\right)\)	\(e\left(\frac{354}{515}\right)\)	\(e\left(\frac{182}{515}\right)\)	\(e\left(\frac{90}{103}\right)\)	\(e\left(\frac{238}{515}\right)\)	\(e\left(\frac{377}{515}\right)\)	\(e\left(\frac{18}{103}\right)\)	\(e\left(\frac{37}{515}\right)\)
\(\chi_{1031}(7,\cdot)\)	1031.f	206	Yes	\(-1\)	\(1\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{90}{103}\right)\)	\(e\left(\frac{127}{206}\right)\)	\(e\left(\frac{86}{103}\right)\)	\(e\left(\frac{54}{103}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{93}{103}\right)\)
\(\chi_{1031}(8,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{249}{515}\right)\)	\(e\left(\frac{504}{515}\right)\)	\(e\left(\frac{498}{515}\right)\)	\(e\left(\frac{146}{515}\right)\)	\(e\left(\frac{238}{515}\right)\)	\(e\left(\frac{86}{103}\right)\)	\(e\left(\frac{232}{515}\right)\)	\(e\left(\frac{493}{515}\right)\)	\(e\left(\frac{79}{103}\right)\)	\(e\left(\frac{88}{515}\right)\)
\(\chi_{1031}(9,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{336}{515}\right)\)	\(e\left(\frac{41}{515}\right)\)	\(e\left(\frac{157}{515}\right)\)	\(e\left(\frac{439}{515}\right)\)	\(e\left(\frac{377}{515}\right)\)	\(e\left(\frac{54}{103}\right)\)	\(e\left(\frac{493}{515}\right)\)	\(e\left(\frac{82}{515}\right)\)	\(e\left(\frac{52}{103}\right)\)	\(e\left(\frac{187}{515}\right)\)
\(\chi_{1031}(10,\cdot)\)	1031.e	103	Yes	\(1\)	\(1\)	\(e\left(\frac{95}{103}\right)\)	\(e\left(\frac{26}{103}\right)\)	\(e\left(\frac{87}{103}\right)\)	\(e\left(\frac{95}{103}\right)\)	\(e\left(\frac{18}{103}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{79}{103}\right)\)	\(e\left(\frac{52}{103}\right)\)	\(e\left(\frac{87}{103}\right)\)	\(e\left(\frac{101}{103}\right)\)
\(\chi_{1031}(11,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{201}{515}\right)\)	\(e\left(\frac{351}{515}\right)\)	\(e\left(\frac{402}{515}\right)\)	\(e\left(\frac{304}{515}\right)\)	\(e\left(\frac{37}{515}\right)\)	\(e\left(\frac{93}{103}\right)\)	\(e\left(\frac{88}{515}\right)\)	\(e\left(\frac{187}{515}\right)\)	\(e\left(\frac{101}{103}\right)\)	\(e\left(\frac{282}{515}\right)\)
\(\chi_{1031}(12,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{334}{515}\right)\)	\(e\left(\frac{99}{515}\right)\)	\(e\left(\frac{153}{515}\right)\)	\(e\left(\frac{231}{515}\right)\)	\(e\left(\frac{433}{515}\right)\)	\(e\left(\frac{50}{103}\right)\)	\(e\left(\frac{487}{515}\right)\)	\(e\left(\frac{198}{515}\right)\)	\(e\left(\frac{10}{103}\right)\)	\(e\left(\frac{238}{515}\right)\)
\(\chi_{1031}(13,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{127}{515}\right)\)	\(e\left(\frac{437}{515}\right)\)	\(e\left(\frac{254}{515}\right)\)	\(e\left(\frac{333}{515}\right)\)	\(e\left(\frac{49}{515}\right)\)	\(e\left(\frac{48}{103}\right)\)	\(e\left(\frac{381}{515}\right)\)	\(e\left(\frac{359}{515}\right)\)	\(e\left(\frac{92}{103}\right)\)	\(e\left(\frac{109}{515}\right)\)
\(\chi_{1031}(14,\cdot)\)	1031.h	1030	Yes	\(-1\)	\(1\)	\(e\left(\frac{398}{515}\right)\)	\(e\left(\frac{303}{515}\right)\)	\(e\left(\frac{281}{515}\right)\)	\(e\left(\frac{192}{515}\right)\)	\(e\left(\frac{186}{515}\right)\)	\(e\left(\frac{47}{206}\right)\)	\(e\left(\frac{164}{515}\right)\)	\(e\left(\frac{91}{515}\right)\)	\(e\left(\frac{15}{103}\right)\)	\(e\left(\frac{151}{515}\right)\)
\(\chi_{1031}(15,\cdot)\)	1031.e	103	Yes	\(1\)	\(1\)	\(e\left(\frac{9}{103}\right)\)	\(e\left(\frac{48}{103}\right)\)	\(e\left(\frac{18}{103}\right)\)	\(e\left(\frac{9}{103}\right)\)	\(e\left(\frac{57}{103}\right)\)	\(e\left(\frac{90}{103}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{96}{103}\right)\)	\(e\left(\frac{18}{103}\right)\)	\(e\left(\frac{28}{103}\right)\)
\(\chi_{1031}(16,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{332}{515}\right)\)	\(e\left(\frac{157}{515}\right)\)	\(e\left(\frac{149}{515}\right)\)	\(e\left(\frac{23}{515}\right)\)	\(e\left(\frac{489}{515}\right)\)	\(e\left(\frac{46}{103}\right)\)	\(e\left(\frac{481}{515}\right)\)	\(e\left(\frac{314}{515}\right)\)	\(e\left(\frac{71}{103}\right)\)	\(e\left(\frac{289}{515}\right)\)
\(\chi_{1031}(17,\cdot)\)	1031.f	206	Yes	\(-1\)	\(1\)	\(e\left(\frac{101}{103}\right)\)	\(e\left(\frac{58}{103}\right)\)	\(e\left(\frac{99}{103}\right)\)	\(e\left(\frac{101}{103}\right)\)	\(e\left(\frac{56}{103}\right)\)	\(e\left(\frac{63}{206}\right)\)	\(e\left(\frac{97}{103}\right)\)	\(e\left(\frac{13}{103}\right)\)	\(e\left(\frac{99}{103}\right)\)	\(e\left(\frac{51}{103}\right)\)
\(\chi_{1031}(18,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{419}{515}\right)\)	\(e\left(\frac{209}{515}\right)\)	\(e\left(\frac{323}{515}\right)\)	\(e\left(\frac{316}{515}\right)\)	\(e\left(\frac{113}{515}\right)\)	\(e\left(\frac{14}{103}\right)\)	\(e\left(\frac{227}{515}\right)\)	\(e\left(\frac{418}{515}\right)\)	\(e\left(\frac{44}{103}\right)\)	\(e\left(\frac{388}{515}\right)\)
\(\chi_{1031}(19,\cdot)\)	1031.f	206	Yes	\(-1\)	\(1\)	\(e\left(\frac{64}{103}\right)\)	\(e\left(\frac{101}{103}\right)\)	\(e\left(\frac{25}{103}\right)\)	\(e\left(\frac{64}{103}\right)\)	\(e\left(\frac{62}{103}\right)\)	\(e\left(\frac{147}{206}\right)\)	\(e\left(\frac{89}{103}\right)\)	\(e\left(\frac{99}{103}\right)\)	\(e\left(\frac{25}{103}\right)\)	\(e\left(\frac{16}{103}\right)\)
\(\chi_{1031}(20,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{43}{515}\right)\)	\(e\left(\frac{298}{515}\right)\)	\(e\left(\frac{86}{515}\right)\)	\(e\left(\frac{352}{515}\right)\)	\(e\left(\frac{341}{515}\right)\)	\(e\left(\frac{86}{103}\right)\)	\(e\left(\frac{129}{515}\right)\)	\(e\left(\frac{81}{515}\right)\)	\(e\left(\frac{79}{103}\right)\)	\(e\left(\frac{191}{515}\right)\)
\(\chi_{1031}(21,\cdot)\)	1031.h	1030	Yes	\(-1\)	\(1\)	\(e\left(\frac{483}{515}\right)\)	\(e\left(\frac{413}{515}\right)\)	\(e\left(\frac{451}{515}\right)\)	\(e\left(\frac{277}{515}\right)\)	\(e\left(\frac{381}{515}\right)\)	\(e\left(\frac{181}{206}\right)\)	\(e\left(\frac{419}{515}\right)\)	\(e\left(\frac{311}{515}\right)\)	\(e\left(\frac{49}{103}\right)\)	\(e\left(\frac{301}{515}\right)\)
\(\chi_{1031}(22,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{284}{515}\right)\)	\(e\left(\frac{4}{515}\right)\)	\(e\left(\frac{53}{515}\right)\)	\(e\left(\frac{181}{515}\right)\)	\(e\left(\frac{288}{515}\right)\)	\(e\left(\frac{53}{103}\right)\)	\(e\left(\frac{337}{515}\right)\)	\(e\left(\frac{8}{515}\right)\)	\(e\left(\frac{93}{103}\right)\)	\(e\left(\frac{483}{515}\right)\)
\(\chi_{1031}(23,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{468}{515}\right)\)	\(e\left(\frac{333}{515}\right)\)	\(e\left(\frac{421}{515}\right)\)	\(e\left(\frac{262}{515}\right)\)	\(e\left(\frac{286}{515}\right)\)	\(e\left(\frac{9}{103}\right)\)	\(e\left(\frac{374}{515}\right)\)	\(e\left(\frac{151}{515}\right)\)	\(e\left(\frac{43}{103}\right)\)	\(e\left(\frac{426}{515}\right)\)
\(\chi_{1031}(24,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{417}{515}\right)\)	\(e\left(\frac{267}{515}\right)\)	\(e\left(\frac{319}{515}\right)\)	\(e\left(\frac{108}{515}\right)\)	\(e\left(\frac{169}{515}\right)\)	\(e\left(\frac{10}{103}\right)\)	\(e\left(\frac{221}{515}\right)\)	\(e\left(\frac{19}{515}\right)\)	\(e\left(\frac{2}{103}\right)\)	\(e\left(\frac{439}{515}\right)\)
\(\chi_{1031}(25,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{269}{515}\right)\)	\(e\left(\frac{439}{515}\right)\)	\(e\left(\frac{23}{515}\right)\)	\(e\left(\frac{166}{515}\right)\)	\(e\left(\frac{193}{515}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{292}{515}\right)\)	\(e\left(\frac{363}{515}\right)\)	\(e\left(\frac{87}{103}\right)\)	\(e\left(\frac{93}{515}\right)\)
\(\chi_{1031}(26,\cdot)\)	1031.e	103	Yes	\(1\)	\(1\)	\(e\left(\frac{42}{103}\right)\)	\(e\left(\frac{18}{103}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{42}{103}\right)\)	\(e\left(\frac{60}{103}\right)\)	\(e\left(\frac{8}{103}\right)\)	\(e\left(\frac{23}{103}\right)\)	\(e\left(\frac{36}{103}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{62}{103}\right)\)
\(\chi_{1031}(27,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{504}{515}\right)\)	\(e\left(\frac{319}{515}\right)\)	\(e\left(\frac{493}{515}\right)\)	\(e\left(\frac{401}{515}\right)\)	\(e\left(\frac{308}{515}\right)\)	\(e\left(\frac{81}{103}\right)\)	\(e\left(\frac{482}{515}\right)\)	\(e\left(\frac{123}{515}\right)\)	\(e\left(\frac{78}{103}\right)\)	\(e\left(\frac{23}{515}\right)\)
\(\chi_{1031}(28,\cdot)\)	1031.h	1030	Yes	\(-1\)	\(1\)	\(e\left(\frac{481}{515}\right)\)	\(e\left(\frac{471}{515}\right)\)	\(e\left(\frac{447}{515}\right)\)	\(e\left(\frac{69}{515}\right)\)	\(e\left(\frac{437}{515}\right)\)	\(e\left(\frac{173}{206}\right)\)	\(e\left(\frac{413}{515}\right)\)	\(e\left(\frac{427}{515}\right)\)	\(e\left(\frac{7}{103}\right)\)	\(e\left(\frac{352}{515}\right)\)
\(\chi_{1031}(29,\cdot)\)	1031.e	103	Yes	\(1\)	\(1\)	\(e\left(\frac{28}{103}\right)\)	\(e\left(\frac{12}{103}\right)\)	\(e\left(\frac{56}{103}\right)\)	\(e\left(\frac{28}{103}\right)\)	\(e\left(\frac{40}{103}\right)\)	\(e\left(\frac{74}{103}\right)\)	\(e\left(\frac{84}{103}\right)\)	\(e\left(\frac{24}{103}\right)\)	\(e\left(\frac{56}{103}\right)\)	\(e\left(\frac{7}{103}\right)\)
\(\chi_{1031}(30,\cdot)\)	1031.g	515	Yes	\(1\)	\(1\)	\(e\left(\frac{128}{515}\right)\)	\(e\left(\frac{408}{515}\right)\)	\(e\left(\frac{256}{515}\right)\)	\(e\left(\frac{437}{515}\right)\)	\(e\left(\frac{21}{515}\right)\)	\(e\left(\frac{50}{103}\right)\)	\(e\left(\frac{384}{515}\right)\)	\(e\left(\frac{301}{515}\right)\)	\(e\left(\frac{10}{103}\right)\)	\(e\left(\frac{341}{515}\right)\)
\(\chi_{1031}(31,\cdot)\)	1031.f	206	Yes	\(-1\)	\(1\)	\(e\left(\frac{79}{103}\right)\)	\(e\left(\frac{78}{103}\right)\)	\(e\left(\frac{55}{103}\right)\)	\(e\left(\frac{79}{103}\right)\)	\(e\left(\frac{54}{103}\right)\)	\(e\left(\frac{35}{206}\right)\)	\(e\left(\frac{31}{103}\right)\)	\(e\left(\frac{53}{103}\right)\)	\(e\left(\frac{55}{103}\right)\)	\(e\left(\frac{97}{103}\right)\)
\(\chi_{1031}(32,\cdot)\)	1031.e	103	Yes	\(1\)	\(1\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{65}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{83}{103}\right)\)	\(e\left(\frac{45}{103}\right)\)	\(e\left(\frac{6}{103}\right)\)	\(e\left(\frac{43}{103}\right)\)	\(e\left(\frac{27}{103}\right)\)	\(e\left(\frac{63}{103}\right)\)	\(e\left(\frac{98}{103}\right)\)

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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.