# Properties

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

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(4031)

pari: g = idealstar(,4031,2)

## Character group

 sage: G.order()  pari: g.no Order = 3864 sage: H.invariants()  pari: g.cyc Structure = $$C_{1932}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4031}(3060,\cdot)$, $\chi_{4031}(4030,\cdot)$

## 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.

orbit label 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 $$-1$$ $$1$$ $$e\left(\frac{148}{161}\right)$$ $$e\left(\frac{19}{161}\right)$$ $$e\left(\frac{135}{161}\right)$$ $$e\left(\frac{78}{161}\right)$$ $$e\left(\frac{6}{161}\right)$$ $$e\left(\frac{40}{161}\right)$$ $$e\left(\frac{122}{161}\right)$$ $$e\left(\frac{38}{161}\right)$$ $$e\left(\frac{65}{161}\right)$$ $$e\left(\frac{71}{322}\right)$$