# Properties

 Modulus 1031 Structure $$C_{1030}$$ Order 1030

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 $$1$$ $$1$$ $$e\left(\frac{83}{103}\right)$$ $$e\left(\frac{65}{103}\right)$$ $$e\left(\frac{63}{103}\right)$$ $$e\left(\frac{83}{103}\right)$$ $$e\left(\frac{45}{103}\right)$$ $$e\left(\frac{6}{103}\right)$$ $$e\left(\frac{43}{103}\right)$$ $$e\left(\frac{27}{103}\right)$$ $$e\left(\frac{63}{103}\right)$$ $$e\left(\frac{98}{103}\right)$$