# Properties

 Modulus 389 Structure $$C_{388}$$ Order 388

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(389)

pari: g = idealstar(,389,2)

## Character group

 sage: G.order()  pari: g.no Order = 388 sage: H.invariants()  pari: g.cyc Structure = $$C_{388}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{389}(2,\cdot)$

## First 32 of 388 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
$$\chi_{389}(1,\cdot)$$ 389.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{389}(2,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{1}{388}\right)$$ $$e\left(\frac{271}{388}\right)$$ $$e\left(\frac{1}{194}\right)$$ $$e\left(\frac{21}{97}\right)$$ $$e\left(\frac{68}{97}\right)$$ $$e\left(\frac{82}{97}\right)$$ $$e\left(\frac{3}{388}\right)$$ $$e\left(\frac{77}{194}\right)$$ $$e\left(\frac{85}{388}\right)$$ $$e\left(\frac{43}{97}\right)$$
$$\chi_{389}(3,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{271}{388}\right)$$ $$e\left(\frac{109}{388}\right)$$ $$e\left(\frac{77}{194}\right)$$ $$e\left(\frac{65}{97}\right)$$ $$e\left(\frac{95}{97}\right)$$ $$e\left(\frac{9}{97}\right)$$ $$e\left(\frac{37}{388}\right)$$ $$e\left(\frac{109}{194}\right)$$ $$e\left(\frac{143}{388}\right)$$ $$e\left(\frac{13}{97}\right)$$
$$\chi_{389}(4,\cdot)$$ 389.e 194 yes $$1$$ $$1$$ $$e\left(\frac{1}{194}\right)$$ $$e\left(\frac{77}{194}\right)$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{42}{97}\right)$$ $$e\left(\frac{39}{97}\right)$$ $$e\left(\frac{67}{97}\right)$$ $$e\left(\frac{3}{194}\right)$$ $$e\left(\frac{77}{97}\right)$$ $$e\left(\frac{85}{194}\right)$$ $$e\left(\frac{86}{97}\right)$$
$$\chi_{389}(5,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{21}{97}\right)$$ $$e\left(\frac{65}{97}\right)$$ $$e\left(\frac{42}{97}\right)$$ $$e\left(\frac{18}{97}\right)$$ $$e\left(\frac{86}{97}\right)$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{63}{97}\right)$$ $$e\left(\frac{33}{97}\right)$$ $$e\left(\frac{39}{97}\right)$$ $$e\left(\frac{23}{97}\right)$$
$$\chi_{389}(6,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{68}{97}\right)$$ $$e\left(\frac{95}{97}\right)$$ $$e\left(\frac{39}{97}\right)$$ $$e\left(\frac{86}{97}\right)$$ $$e\left(\frac{66}{97}\right)$$ $$e\left(\frac{91}{97}\right)$$ $$e\left(\frac{10}{97}\right)$$ $$e\left(\frac{93}{97}\right)$$ $$e\left(\frac{57}{97}\right)$$ $$e\left(\frac{56}{97}\right)$$
$$\chi_{389}(7,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{82}{97}\right)$$ $$e\left(\frac{9}{97}\right)$$ $$e\left(\frac{67}{97}\right)$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{91}{97}\right)$$ $$e\left(\frac{27}{97}\right)$$ $$e\left(\frac{52}{97}\right)$$ $$e\left(\frac{18}{97}\right)$$ $$e\left(\frac{83}{97}\right)$$ $$e\left(\frac{39}{97}\right)$$
$$\chi_{389}(8,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{3}{388}\right)$$ $$e\left(\frac{37}{388}\right)$$ $$e\left(\frac{3}{194}\right)$$ $$e\left(\frac{63}{97}\right)$$ $$e\left(\frac{10}{97}\right)$$ $$e\left(\frac{52}{97}\right)$$ $$e\left(\frac{9}{388}\right)$$ $$e\left(\frac{37}{194}\right)$$ $$e\left(\frac{255}{388}\right)$$ $$e\left(\frac{32}{97}\right)$$
$$\chi_{389}(9,\cdot)$$ 389.e 194 yes $$1$$ $$1$$ $$e\left(\frac{77}{194}\right)$$ $$e\left(\frac{109}{194}\right)$$ $$e\left(\frac{77}{97}\right)$$ $$e\left(\frac{33}{97}\right)$$ $$e\left(\frac{93}{97}\right)$$ $$e\left(\frac{18}{97}\right)$$ $$e\left(\frac{37}{194}\right)$$ $$e\left(\frac{12}{97}\right)$$ $$e\left(\frac{143}{194}\right)$$ $$e\left(\frac{26}{97}\right)$$
$$\chi_{389}(10,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{85}{388}\right)$$ $$e\left(\frac{143}{388}\right)$$ $$e\left(\frac{85}{194}\right)$$ $$e\left(\frac{39}{97}\right)$$ $$e\left(\frac{57}{97}\right)$$ $$e\left(\frac{83}{97}\right)$$ $$e\left(\frac{255}{388}\right)$$ $$e\left(\frac{143}{194}\right)$$ $$e\left(\frac{241}{388}\right)$$ $$e\left(\frac{66}{97}\right)$$
$$\chi_{389}(11,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{43}{97}\right)$$ $$e\left(\frac{13}{97}\right)$$ $$e\left(\frac{86}{97}\right)$$ $$e\left(\frac{23}{97}\right)$$ $$e\left(\frac{56}{97}\right)$$ $$e\left(\frac{39}{97}\right)$$ $$e\left(\frac{32}{97}\right)$$ $$e\left(\frac{26}{97}\right)$$ $$e\left(\frac{66}{97}\right)$$ $$e\left(\frac{24}{97}\right)$$
$$\chi_{389}(12,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{273}{388}\right)$$ $$e\left(\frac{263}{388}\right)$$ $$e\left(\frac{79}{194}\right)$$ $$e\left(\frac{10}{97}\right)$$ $$e\left(\frac{37}{97}\right)$$ $$e\left(\frac{76}{97}\right)$$ $$e\left(\frac{43}{388}\right)$$ $$e\left(\frac{69}{194}\right)$$ $$e\left(\frac{313}{388}\right)$$ $$e\left(\frac{2}{97}\right)$$
$$\chi_{389}(13,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{8}{97}\right)$$ $$e\left(\frac{34}{97}\right)$$ $$e\left(\frac{16}{97}\right)$$ $$e\left(\frac{90}{97}\right)$$ $$e\left(\frac{42}{97}\right)$$ $$e\left(\frac{5}{97}\right)$$ $$e\left(\frac{24}{97}\right)$$ $$e\left(\frac{68}{97}\right)$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{18}{97}\right)$$
$$\chi_{389}(14,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{329}{388}\right)$$ $$e\left(\frac{307}{388}\right)$$ $$e\left(\frac{135}{194}\right)$$ $$e\left(\frac{22}{97}\right)$$ $$e\left(\frac{62}{97}\right)$$ $$e\left(\frac{12}{97}\right)$$ $$e\left(\frac{211}{388}\right)$$ $$e\left(\frac{113}{194}\right)$$ $$e\left(\frac{29}{388}\right)$$ $$e\left(\frac{82}{97}\right)$$
$$\chi_{389}(15,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{355}{388}\right)$$ $$e\left(\frac{369}{388}\right)$$ $$e\left(\frac{161}{194}\right)$$ $$e\left(\frac{83}{97}\right)$$ $$e\left(\frac{84}{97}\right)$$ $$e\left(\frac{10}{97}\right)$$ $$e\left(\frac{289}{388}\right)$$ $$e\left(\frac{175}{194}\right)$$ $$e\left(\frac{299}{388}\right)$$ $$e\left(\frac{36}{97}\right)$$
$$\chi_{389}(16,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{77}{97}\right)$$ $$e\left(\frac{2}{97}\right)$$ $$e\left(\frac{84}{97}\right)$$ $$e\left(\frac{78}{97}\right)$$ $$e\left(\frac{37}{97}\right)$$ $$e\left(\frac{3}{97}\right)$$ $$e\left(\frac{57}{97}\right)$$ $$e\left(\frac{85}{97}\right)$$ $$e\left(\frac{75}{97}\right)$$
$$\chi_{389}(17,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{94}{97}\right)$$ $$e\left(\frac{60}{97}\right)$$ $$e\left(\frac{91}{97}\right)$$ $$e\left(\frac{39}{97}\right)$$ $$e\left(\frac{57}{97}\right)$$ $$e\left(\frac{83}{97}\right)$$ $$e\left(\frac{88}{97}\right)$$ $$e\left(\frac{23}{97}\right)$$ $$e\left(\frac{36}{97}\right)$$ $$e\left(\frac{66}{97}\right)$$
$$\chi_{389}(18,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{155}{388}\right)$$ $$e\left(\frac{101}{388}\right)$$ $$e\left(\frac{155}{194}\right)$$ $$e\left(\frac{54}{97}\right)$$ $$e\left(\frac{64}{97}\right)$$ $$e\left(\frac{3}{97}\right)$$ $$e\left(\frac{77}{388}\right)$$ $$e\left(\frac{101}{194}\right)$$ $$e\left(\frac{371}{388}\right)$$ $$e\left(\frac{69}{97}\right)$$
$$\chi_{389}(19,\cdot)$$ 389.e 194 yes $$1$$ $$1$$ $$e\left(\frac{131}{194}\right)$$ $$e\left(\frac{193}{194}\right)$$ $$e\left(\frac{34}{97}\right)$$ $$e\left(\frac{70}{97}\right)$$ $$e\left(\frac{65}{97}\right)$$ $$e\left(\frac{47}{97}\right)$$ $$e\left(\frac{5}{194}\right)$$ $$e\left(\frac{96}{97}\right)$$ $$e\left(\frac{77}{194}\right)$$ $$e\left(\frac{14}{97}\right)$$
$$\chi_{389}(20,\cdot)$$ 389.e 194 yes $$1$$ $$1$$ $$e\left(\frac{43}{194}\right)$$ $$e\left(\frac{13}{194}\right)$$ $$e\left(\frac{43}{97}\right)$$ $$e\left(\frac{60}{97}\right)$$ $$e\left(\frac{28}{97}\right)$$ $$e\left(\frac{68}{97}\right)$$ $$e\left(\frac{129}{194}\right)$$ $$e\left(\frac{13}{97}\right)$$ $$e\left(\frac{163}{194}\right)$$ $$e\left(\frac{12}{97}\right)$$
$$\chi_{389}(21,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{211}{388}\right)$$ $$e\left(\frac{145}{388}\right)$$ $$e\left(\frac{17}{194}\right)$$ $$e\left(\frac{66}{97}\right)$$ $$e\left(\frac{89}{97}\right)$$ $$e\left(\frac{36}{97}\right)$$ $$e\left(\frac{245}{388}\right)$$ $$e\left(\frac{145}{194}\right)$$ $$e\left(\frac{87}{388}\right)$$ $$e\left(\frac{52}{97}\right)$$
$$\chi_{389}(22,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{173}{388}\right)$$ $$e\left(\frac{323}{388}\right)$$ $$e\left(\frac{173}{194}\right)$$ $$e\left(\frac{44}{97}\right)$$ $$e\left(\frac{27}{97}\right)$$ $$e\left(\frac{24}{97}\right)$$ $$e\left(\frac{131}{388}\right)$$ $$e\left(\frac{129}{194}\right)$$ $$e\left(\frac{349}{388}\right)$$ $$e\left(\frac{67}{97}\right)$$
$$\chi_{389}(23,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{13}{388}\right)$$ $$e\left(\frac{31}{388}\right)$$ $$e\left(\frac{13}{194}\right)$$ $$e\left(\frac{79}{97}\right)$$ $$e\left(\frac{11}{97}\right)$$ $$e\left(\frac{96}{97}\right)$$ $$e\left(\frac{39}{388}\right)$$ $$e\left(\frac{31}{194}\right)$$ $$e\left(\frac{329}{388}\right)$$ $$e\left(\frac{74}{97}\right)$$
$$\chi_{389}(24,\cdot)$$ 389.e 194 yes $$1$$ $$1$$ $$e\left(\frac{137}{194}\right)$$ $$e\left(\frac{73}{194}\right)$$ $$e\left(\frac{40}{97}\right)$$ $$e\left(\frac{31}{97}\right)$$ $$e\left(\frac{8}{97}\right)$$ $$e\left(\frac{61}{97}\right)$$ $$e\left(\frac{23}{194}\right)$$ $$e\left(\frac{73}{97}\right)$$ $$e\left(\frac{5}{194}\right)$$ $$e\left(\frac{45}{97}\right)$$
$$\chi_{389}(25,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{42}{97}\right)$$ $$e\left(\frac{33}{97}\right)$$ $$e\left(\frac{84}{97}\right)$$ $$e\left(\frac{36}{97}\right)$$ $$e\left(\frac{75}{97}\right)$$ $$e\left(\frac{2}{97}\right)$$ $$e\left(\frac{29}{97}\right)$$ $$e\left(\frac{66}{97}\right)$$ $$e\left(\frac{78}{97}\right)$$ $$e\left(\frac{46}{97}\right)$$
$$\chi_{389}(26,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{33}{388}\right)$$ $$e\left(\frac{19}{388}\right)$$ $$e\left(\frac{33}{194}\right)$$ $$e\left(\frac{14}{97}\right)$$ $$e\left(\frac{13}{97}\right)$$ $$e\left(\frac{87}{97}\right)$$ $$e\left(\frac{99}{388}\right)$$ $$e\left(\frac{19}{194}\right)$$ $$e\left(\frac{89}{388}\right)$$ $$e\left(\frac{61}{97}\right)$$
$$\chi_{389}(27,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{37}{388}\right)$$ $$e\left(\frac{327}{388}\right)$$ $$e\left(\frac{37}{194}\right)$$ $$e\left(\frac{1}{97}\right)$$ $$e\left(\frac{91}{97}\right)$$ $$e\left(\frac{27}{97}\right)$$ $$e\left(\frac{111}{388}\right)$$ $$e\left(\frac{133}{194}\right)$$ $$e\left(\frac{41}{388}\right)$$ $$e\left(\frac{39}{97}\right)$$
$$\chi_{389}(28,\cdot)$$ 389.e 194 yes $$1$$ $$1$$ $$e\left(\frac{165}{194}\right)$$ $$e\left(\frac{95}{194}\right)$$ $$e\left(\frac{68}{97}\right)$$ $$e\left(\frac{43}{97}\right)$$ $$e\left(\frac{33}{97}\right)$$ $$e\left(\frac{94}{97}\right)$$ $$e\left(\frac{107}{194}\right)$$ $$e\left(\frac{95}{97}\right)$$ $$e\left(\frac{57}{194}\right)$$ $$e\left(\frac{28}{97}\right)$$
$$\chi_{389}(29,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{47}{388}\right)$$ $$e\left(\frac{321}{388}\right)$$ $$e\left(\frac{47}{194}\right)$$ $$e\left(\frac{17}{97}\right)$$ $$e\left(\frac{92}{97}\right)$$ $$e\left(\frac{71}{97}\right)$$ $$e\left(\frac{141}{388}\right)$$ $$e\left(\frac{127}{194}\right)$$ $$e\left(\frac{115}{388}\right)$$ $$e\left(\frac{81}{97}\right)$$
$$\chi_{389}(30,\cdot)$$ 389.d 97 yes $$1$$ $$1$$ $$e\left(\frac{89}{97}\right)$$ $$e\left(\frac{63}{97}\right)$$ $$e\left(\frac{81}{97}\right)$$ $$e\left(\frac{7}{97}\right)$$ $$e\left(\frac{55}{97}\right)$$ $$e\left(\frac{92}{97}\right)$$ $$e\left(\frac{73}{97}\right)$$ $$e\left(\frac{29}{97}\right)$$ $$e\left(\frac{96}{97}\right)$$ $$e\left(\frac{79}{97}\right)$$
$$\chi_{389}(31,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{297}{388}\right)$$ $$e\left(\frac{171}{388}\right)$$ $$e\left(\frac{103}{194}\right)$$ $$e\left(\frac{29}{97}\right)$$ $$e\left(\frac{20}{97}\right)$$ $$e\left(\frac{7}{97}\right)$$ $$e\left(\frac{115}{388}\right)$$ $$e\left(\frac{171}{194}\right)$$ $$e\left(\frac{25}{388}\right)$$ $$e\left(\frac{64}{97}\right)$$
$$\chi_{389}(32,\cdot)$$ 389.f 388 yes $$-1$$ $$1$$ $$e\left(\frac{5}{388}\right)$$ $$e\left(\frac{191}{388}\right)$$ $$e\left(\frac{5}{194}\right)$$ $$e\left(\frac{8}{97}\right)$$ $$e\left(\frac{49}{97}\right)$$ $$e\left(\frac{22}{97}\right)$$ $$e\left(\frac{15}{388}\right)$$ $$e\left(\frac{191}{194}\right)$$ $$e\left(\frac{37}{388}\right)$$ $$e\left(\frac{21}{97}\right)$$