# Properties

 Modulus 4023 Structure $$C_{1332}\times C_{2}$$ Order 2664

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4023)

pari: g = idealstar(,4023,2)

## Character group

 sage: G.order()  pari: g.no Order = 2664 sage: H.invariants()  pari: g.cyc Structure = $$C_{1332}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4023}(3578,\cdot)$, $\chi_{4023}(3428,\cdot)$

## First 32 of 2664 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 4 5 7 8 10 11 13 14 16
$$\chi_{4023}(1,\cdot)$$ 4023.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4023}(2,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{83}{1332}\right)$$ $$e\left(\frac{83}{666}\right)$$ $$e\left(\frac{653}{666}\right)$$ $$e\left(\frac{565}{666}\right)$$ $$e\left(\frac{83}{444}\right)$$ $$e\left(\frac{19}{444}\right)$$ $$e\left(\frac{611}{1332}\right)$$ $$e\left(\frac{1069}{1332}\right)$$ $$e\left(\frac{1213}{1332}\right)$$ $$e\left(\frac{83}{333}\right)$$
$$\chi_{4023}(4,\cdot)$$ 4023.bf 666 yes $$1$$ $$1$$ $$e\left(\frac{83}{666}\right)$$ $$e\left(\frac{83}{333}\right)$$ $$e\left(\frac{320}{333}\right)$$ $$e\left(\frac{232}{333}\right)$$ $$e\left(\frac{83}{222}\right)$$ $$e\left(\frac{19}{222}\right)$$ $$e\left(\frac{611}{666}\right)$$ $$e\left(\frac{403}{666}\right)$$ $$e\left(\frac{547}{666}\right)$$ $$e\left(\frac{166}{333}\right)$$
$$\chi_{4023}(5,\cdot)$$ 4023.bg 666 yes $$-1$$ $$1$$ $$e\left(\frac{653}{666}\right)$$ $$e\left(\frac{320}{333}\right)$$ $$e\left(\frac{313}{666}\right)$$ $$e\left(\frac{76}{333}\right)$$ $$e\left(\frac{209}{222}\right)$$ $$e\left(\frac{50}{111}\right)$$ $$e\left(\frac{137}{666}\right)$$ $$e\left(\frac{155}{333}\right)$$ $$e\left(\frac{139}{666}\right)$$ $$e\left(\frac{307}{333}\right)$$
$$\chi_{4023}(7,\cdot)$$ 4023.bf 666 yes $$1$$ $$1$$ $$e\left(\frac{565}{666}\right)$$ $$e\left(\frac{232}{333}\right)$$ $$e\left(\frac{76}{333}\right)$$ $$e\left(\frac{155}{333}\right)$$ $$e\left(\frac{121}{222}\right)$$ $$e\left(\frac{17}{222}\right)$$ $$e\left(\frac{91}{666}\right)$$ $$e\left(\frac{641}{666}\right)$$ $$e\left(\frac{209}{666}\right)$$ $$e\left(\frac{131}{333}\right)$$
$$\chi_{4023}(8,\cdot)$$ 4023.bd 444 no $$1$$ $$1$$ $$e\left(\frac{83}{444}\right)$$ $$e\left(\frac{83}{222}\right)$$ $$e\left(\frac{209}{222}\right)$$ $$e\left(\frac{121}{222}\right)$$ $$e\left(\frac{83}{148}\right)$$ $$e\left(\frac{19}{148}\right)$$ $$e\left(\frac{167}{444}\right)$$ $$e\left(\frac{181}{444}\right)$$ $$e\left(\frac{325}{444}\right)$$ $$e\left(\frac{83}{111}\right)$$
$$\chi_{4023}(10,\cdot)$$ 4023.be 444 no $$-1$$ $$1$$ $$e\left(\frac{19}{444}\right)$$ $$e\left(\frac{19}{222}\right)$$ $$e\left(\frac{50}{111}\right)$$ $$e\left(\frac{17}{222}\right)$$ $$e\left(\frac{19}{148}\right)$$ $$e\left(\frac{73}{148}\right)$$ $$e\left(\frac{295}{444}\right)$$ $$e\left(\frac{119}{444}\right)$$ $$e\left(\frac{53}{444}\right)$$ $$e\left(\frac{19}{111}\right)$$
$$\chi_{4023}(11,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{611}{1332}\right)$$ $$e\left(\frac{611}{666}\right)$$ $$e\left(\frac{137}{666}\right)$$ $$e\left(\frac{91}{666}\right)$$ $$e\left(\frac{167}{444}\right)$$ $$e\left(\frac{295}{444}\right)$$ $$e\left(\frac{887}{1332}\right)$$ $$e\left(\frac{1081}{1332}\right)$$ $$e\left(\frac{793}{1332}\right)$$ $$e\left(\frac{278}{333}\right)$$
$$\chi_{4023}(13,\cdot)$$ 4023.bj 1332 yes $$-1$$ $$1$$ $$e\left(\frac{1069}{1332}\right)$$ $$e\left(\frac{403}{666}\right)$$ $$e\left(\frac{155}{333}\right)$$ $$e\left(\frac{641}{666}\right)$$ $$e\left(\frac{181}{444}\right)$$ $$e\left(\frac{119}{444}\right)$$ $$e\left(\frac{1081}{1332}\right)$$ $$e\left(\frac{713}{1332}\right)$$ $$e\left(\frac{1019}{1332}\right)$$ $$e\left(\frac{70}{333}\right)$$
$$\chi_{4023}(14,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{1213}{1332}\right)$$ $$e\left(\frac{547}{666}\right)$$ $$e\left(\frac{139}{666}\right)$$ $$e\left(\frac{209}{666}\right)$$ $$e\left(\frac{325}{444}\right)$$ $$e\left(\frac{53}{444}\right)$$ $$e\left(\frac{793}{1332}\right)$$ $$e\left(\frac{1019}{1332}\right)$$ $$e\left(\frac{299}{1332}\right)$$ $$e\left(\frac{214}{333}\right)$$
$$\chi_{4023}(16,\cdot)$$ 4023.bc 333 yes $$1$$ $$1$$ $$e\left(\frac{83}{333}\right)$$ $$e\left(\frac{166}{333}\right)$$ $$e\left(\frac{307}{333}\right)$$ $$e\left(\frac{131}{333}\right)$$ $$e\left(\frac{83}{111}\right)$$ $$e\left(\frac{19}{111}\right)$$ $$e\left(\frac{278}{333}\right)$$ $$e\left(\frac{70}{333}\right)$$ $$e\left(\frac{214}{333}\right)$$ $$e\left(\frac{332}{333}\right)$$
$$\chi_{4023}(17,\cdot)$$ 4023.z 222 no $$-1$$ $$1$$ $$e\left(\frac{149}{222}\right)$$ $$e\left(\frac{38}{111}\right)$$ $$e\left(\frac{67}{222}\right)$$ $$e\left(\frac{34}{111}\right)$$ $$e\left(\frac{1}{74}\right)$$ $$e\left(\frac{36}{37}\right)$$ $$e\left(\frac{35}{222}\right)$$ $$e\left(\frac{8}{111}\right)$$ $$e\left(\frac{217}{222}\right)$$ $$e\left(\frac{76}{111}\right)$$
$$\chi_{4023}(19,\cdot)$$ 4023.w 111 no $$1$$ $$1$$ $$e\left(\frac{26}{111}\right)$$ $$e\left(\frac{52}{111}\right)$$ $$e\left(\frac{40}{111}\right)$$ $$e\left(\frac{29}{111}\right)$$ $$e\left(\frac{26}{37}\right)$$ $$e\left(\frac{22}{37}\right)$$ $$e\left(\frac{59}{111}\right)$$ $$e\left(\frac{46}{111}\right)$$ $$e\left(\frac{55}{111}\right)$$ $$e\left(\frac{104}{111}\right)$$
$$\chi_{4023}(20,\cdot)$$ 4023.bh 666 yes $$-1$$ $$1$$ $$e\left(\frac{35}{333}\right)$$ $$e\left(\frac{70}{333}\right)$$ $$e\left(\frac{287}{666}\right)$$ $$e\left(\frac{308}{333}\right)$$ $$e\left(\frac{35}{111}\right)$$ $$e\left(\frac{119}{222}\right)$$ $$e\left(\frac{41}{333}\right)$$ $$e\left(\frac{47}{666}\right)$$ $$e\left(\frac{10}{333}\right)$$ $$e\left(\frac{140}{333}\right)$$
$$\chi_{4023}(22,\cdot)$$ 4023.bf 666 yes $$1$$ $$1$$ $$e\left(\frac{347}{666}\right)$$ $$e\left(\frac{14}{333}\right)$$ $$e\left(\frac{62}{333}\right)$$ $$e\left(\frac{328}{333}\right)$$ $$e\left(\frac{125}{222}\right)$$ $$e\left(\frac{157}{222}\right)$$ $$e\left(\frac{83}{666}\right)$$ $$e\left(\frac{409}{666}\right)$$ $$e\left(\frac{337}{666}\right)$$ $$e\left(\frac{28}{333}\right)$$
$$\chi_{4023}(23,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{337}{1332}\right)$$ $$e\left(\frac{337}{666}\right)$$ $$e\left(\frac{541}{666}\right)$$ $$e\left(\frac{617}{666}\right)$$ $$e\left(\frac{337}{444}\right)$$ $$e\left(\frac{29}{444}\right)$$ $$e\left(\frac{1213}{1332}\right)$$ $$e\left(\frac{1211}{1332}\right)$$ $$e\left(\frac{239}{1332}\right)$$ $$e\left(\frac{4}{333}\right)$$
$$\chi_{4023}(25,\cdot)$$ 4023.bc 333 yes $$1$$ $$1$$ $$e\left(\frac{320}{333}\right)$$ $$e\left(\frac{307}{333}\right)$$ $$e\left(\frac{313}{333}\right)$$ $$e\left(\frac{152}{333}\right)$$ $$e\left(\frac{98}{111}\right)$$ $$e\left(\frac{100}{111}\right)$$ $$e\left(\frac{137}{333}\right)$$ $$e\left(\frac{310}{333}\right)$$ $$e\left(\frac{139}{333}\right)$$ $$e\left(\frac{281}{333}\right)$$
$$\chi_{4023}(26,\cdot)$$ 4023.t 74 no $$-1$$ $$1$$ $$e\left(\frac{32}{37}\right)$$ $$e\left(\frac{27}{37}\right)$$ $$e\left(\frac{33}{74}\right)$$ $$e\left(\frac{30}{37}\right)$$ $$e\left(\frac{22}{37}\right)$$ $$e\left(\frac{23}{74}\right)$$ $$e\left(\frac{10}{37}\right)$$ $$e\left(\frac{25}{74}\right)$$ $$e\left(\frac{25}{37}\right)$$ $$e\left(\frac{17}{37}\right)$$
$$\chi_{4023}(28,\cdot)$$ 4023.s 37 no $$1$$ $$1$$ $$e\left(\frac{36}{37}\right)$$ $$e\left(\frac{35}{37}\right)$$ $$e\left(\frac{7}{37}\right)$$ $$e\left(\frac{6}{37}\right)$$ $$e\left(\frac{34}{37}\right)$$ $$e\left(\frac{6}{37}\right)$$ $$e\left(\frac{2}{37}\right)$$ $$e\left(\frac{21}{37}\right)$$ $$e\left(\frac{5}{37}\right)$$ $$e\left(\frac{33}{37}\right)$$
$$\chi_{4023}(29,\cdot)$$ 4023.bg 666 yes $$-1$$ $$1$$ $$e\left(\frac{577}{666}\right)$$ $$e\left(\frac{244}{333}\right)$$ $$e\left(\frac{401}{666}\right)$$ $$e\left(\frac{8}{333}\right)$$ $$e\left(\frac{133}{222}\right)$$ $$e\left(\frac{52}{111}\right)$$ $$e\left(\frac{67}{666}\right)$$ $$e\left(\frac{139}{333}\right)$$ $$e\left(\frac{593}{666}\right)$$ $$e\left(\frac{155}{333}\right)$$
$$\chi_{4023}(31,\cdot)$$ 4023.bc 333 yes $$1$$ $$1$$ $$e\left(\frac{1}{333}\right)$$ $$e\left(\frac{2}{333}\right)$$ $$e\left(\frac{104}{333}\right)$$ $$e\left(\frac{142}{333}\right)$$ $$e\left(\frac{1}{111}\right)$$ $$e\left(\frac{35}{111}\right)$$ $$e\left(\frac{220}{333}\right)$$ $$e\left(\frac{53}{333}\right)$$ $$e\left(\frac{143}{333}\right)$$ $$e\left(\frac{4}{333}\right)$$
$$\chi_{4023}(32,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{415}{1332}\right)$$ $$e\left(\frac{415}{666}\right)$$ $$e\left(\frac{601}{666}\right)$$ $$e\left(\frac{161}{666}\right)$$ $$e\left(\frac{415}{444}\right)$$ $$e\left(\frac{95}{444}\right)$$ $$e\left(\frac{391}{1332}\right)$$ $$e\left(\frac{17}{1332}\right)$$ $$e\left(\frac{737}{1332}\right)$$ $$e\left(\frac{82}{333}\right)$$
$$\chi_{4023}(34,\cdot)$$ 4023.bj 1332 yes $$-1$$ $$1$$ $$e\left(\frac{977}{1332}\right)$$ $$e\left(\frac{311}{666}\right)$$ $$e\left(\frac{94}{333}\right)$$ $$e\left(\frac{103}{666}\right)$$ $$e\left(\frac{89}{444}\right)$$ $$e\left(\frac{7}{444}\right)$$ $$e\left(\frac{821}{1332}\right)$$ $$e\left(\frac{1165}{1332}\right)$$ $$e\left(\frac{1183}{1332}\right)$$ $$e\left(\frac{311}{333}\right)$$
$$\chi_{4023}(35,\cdot)$$ 4023.bb 222 no $$-1$$ $$1$$ $$e\left(\frac{92}{111}\right)$$ $$e\left(\frac{73}{111}\right)$$ $$e\left(\frac{155}{222}\right)$$ $$e\left(\frac{77}{111}\right)$$ $$e\left(\frac{18}{37}\right)$$ $$e\left(\frac{39}{74}\right)$$ $$e\left(\frac{38}{111}\right)$$ $$e\left(\frac{95}{222}\right)$$ $$e\left(\frac{58}{111}\right)$$ $$e\left(\frac{35}{111}\right)$$
$$\chi_{4023}(37,\cdot)$$ 4023.w 111 no $$1$$ $$1$$ $$e\left(\frac{91}{111}\right)$$ $$e\left(\frac{71}{111}\right)$$ $$e\left(\frac{29}{111}\right)$$ $$e\left(\frac{46}{111}\right)$$ $$e\left(\frac{17}{37}\right)$$ $$e\left(\frac{3}{37}\right)$$ $$e\left(\frac{40}{111}\right)$$ $$e\left(\frac{50}{111}\right)$$ $$e\left(\frac{26}{111}\right)$$ $$e\left(\frac{31}{111}\right)$$
$$\chi_{4023}(38,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{395}{1332}\right)$$ $$e\left(\frac{395}{666}\right)$$ $$e\left(\frac{227}{666}\right)$$ $$e\left(\frac{73}{666}\right)$$ $$e\left(\frac{395}{444}\right)$$ $$e\left(\frac{283}{444}\right)$$ $$e\left(\frac{1319}{1332}\right)$$ $$e\left(\frac{289}{1332}\right)$$ $$e\left(\frac{541}{1332}\right)$$ $$e\left(\frac{62}{333}\right)$$
$$\chi_{4023}(40,\cdot)$$ 4023.bj 1332 yes $$-1$$ $$1$$ $$e\left(\frac{223}{1332}\right)$$ $$e\left(\frac{223}{666}\right)$$ $$e\left(\frac{137}{333}\right)$$ $$e\left(\frac{515}{666}\right)$$ $$e\left(\frac{223}{444}\right)$$ $$e\left(\frac{257}{444}\right)$$ $$e\left(\frac{775}{1332}\right)$$ $$e\left(\frac{1163}{1332}\right)$$ $$e\left(\frac{1253}{1332}\right)$$ $$e\left(\frac{223}{333}\right)$$
$$\chi_{4023}(41,\cdot)$$ 4023.bi 1332 yes $$1$$ $$1$$ $$e\left(\frac{295}{1332}\right)$$ $$e\left(\frac{295}{666}\right)$$ $$e\left(\frac{355}{666}\right)$$ $$e\left(\frac{299}{666}\right)$$ $$e\left(\frac{295}{444}\right)$$ $$e\left(\frac{335}{444}\right)$$ $$e\left(\frac{631}{1332}\right)$$ $$e\left(\frac{317}{1332}\right)$$ $$e\left(\frac{893}{1332}\right)$$ $$e\left(\frac{295}{333}\right)$$
$$\chi_{4023}(43,\cdot)$$ 4023.bj 1332 yes $$-1$$ $$1$$ $$e\left(\frac{1133}{1332}\right)$$ $$e\left(\frac{467}{666}\right)$$ $$e\left(\frac{154}{333}\right)$$ $$e\left(\frac{523}{666}\right)$$ $$e\left(\frac{245}{444}\right)$$ $$e\left(\frac{139}{444}\right)$$ $$e\left(\frac{509}{1332}\right)$$ $$e\left(\frac{109}{1332}\right)$$ $$e\left(\frac{847}{1332}\right)$$ $$e\left(\frac{134}{333}\right)$$
$$\chi_{4023}(44,\cdot)$$ 4023.m 12 no $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{4023}(46,\cdot)$$ 4023.w 111 no $$1$$ $$1$$ $$e\left(\frac{35}{111}\right)$$ $$e\left(\frac{70}{111}\right)$$ $$e\left(\frac{88}{111}\right)$$ $$e\left(\frac{86}{111}\right)$$ $$e\left(\frac{35}{37}\right)$$ $$e\left(\frac{4}{37}\right)$$ $$e\left(\frac{41}{111}\right)$$ $$e\left(\frac{79}{111}\right)$$ $$e\left(\frac{10}{111}\right)$$ $$e\left(\frac{29}{111}\right)$$
$$\chi_{4023}(47,\cdot)$$ 4023.bh 666 yes $$-1$$ $$1$$ $$e\left(\frac{107}{333}\right)$$ $$e\left(\frac{214}{333}\right)$$ $$e\left(\frac{611}{666}\right)$$ $$e\left(\frac{209}{333}\right)$$ $$e\left(\frac{107}{111}\right)$$ $$e\left(\frac{53}{222}\right)$$ $$e\left(\frac{230}{333}\right)$$ $$e\left(\frac{353}{666}\right)$$ $$e\left(\frac{316}{333}\right)$$ $$e\left(\frac{95}{333}\right)$$