# Properties

 Modulus $6003$ Structure $$C_{924}\times C_{2}\times C_{2}$$ Order $3696$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(6003)

pari: g = idealstar(,6003,2)

## Character group

 sage: G.order()  pari: g.no Order = 3696 sage: H.invariants()  pari: g.cyc Structure = $$C_{924}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6003}(668,\cdot)$, $\chi_{6003}(3133,\cdot)$, $\chi_{6003}(4555,\cdot)$

## First 32 of 3696 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.

Character Orbit Order Primitive $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{6003}(1,\cdot)$$ 6003.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6003}(2,\cdot)$$ 6003.do 924 yes $$1$$ $$1$$ $$e\left(\frac{355}{924}\right)$$ $$e\left(\frac{355}{462}\right)$$ $$e\left(\frac{164}{231}\right)$$ $$e\left(\frac{190}{231}\right)$$ $$e\left(\frac{47}{308}\right)$$ $$e\left(\frac{29}{308}\right)$$ $$e\left(\frac{811}{924}\right)$$ $$e\left(\frac{115}{462}\right)$$ $$e\left(\frac{191}{924}\right)$$ $$e\left(\frac{124}{231}\right)$$
$$\chi_{6003}(4,\cdot)$$ 6003.dk 462 yes $$1$$ $$1$$ $$e\left(\frac{355}{462}\right)$$ $$e\left(\frac{124}{231}\right)$$ $$e\left(\frac{97}{231}\right)$$ $$e\left(\frac{149}{231}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{29}{154}\right)$$ $$e\left(\frac{349}{462}\right)$$ $$e\left(\frac{115}{231}\right)$$ $$e\left(\frac{191}{462}\right)$$ $$e\left(\frac{17}{231}\right)$$
$$\chi_{6003}(5,\cdot)$$ 6003.dh 462 yes $$1$$ $$1$$ $$e\left(\frac{164}{231}\right)$$ $$e\left(\frac{97}{231}\right)$$ $$e\left(\frac{115}{231}\right)$$ $$e\left(\frac{289}{462}\right)$$ $$e\left(\frac{10}{77}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{409}{462}\right)$$ $$e\left(\frac{103}{231}\right)$$ $$e\left(\frac{155}{462}\right)$$ $$e\left(\frac{194}{231}\right)$$
$$\chi_{6003}(7,\cdot)$$ 6003.dj 462 yes $$-1$$ $$1$$ $$e\left(\frac{190}{231}\right)$$ $$e\left(\frac{149}{231}\right)$$ $$e\left(\frac{289}{462}\right)$$ $$e\left(\frac{101}{462}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{69}{154}\right)$$ $$e\left(\frac{71}{462}\right)$$ $$e\left(\frac{32}{231}\right)$$ $$e\left(\frac{19}{462}\right)$$ $$e\left(\frac{67}{231}\right)$$
$$\chi_{6003}(8,\cdot)$$ 6003.dg 308 no $$1$$ $$1$$ $$e\left(\frac{47}{308}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{10}{77}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{141}{308}\right)$$ $$e\left(\frac{87}{308}\right)$$ $$e\left(\frac{195}{308}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{191}{308}\right)$$ $$e\left(\frac{47}{77}\right)$$
$$\chi_{6003}(10,\cdot)$$ 6003.df 308 no $$1$$ $$1$$ $$e\left(\frac{29}{308}\right)$$ $$e\left(\frac{29}{154}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{69}{154}\right)$$ $$e\left(\frac{87}{308}\right)$$ $$e\left(\frac{93}{308}\right)$$ $$e\left(\frac{235}{308}\right)$$ $$e\left(\frac{107}{154}\right)$$ $$e\left(\frac{167}{308}\right)$$ $$e\left(\frac{29}{77}\right)$$
$$\chi_{6003}(11,\cdot)$$ 6003.dr 924 yes $$-1$$ $$1$$ $$e\left(\frac{811}{924}\right)$$ $$e\left(\frac{349}{462}\right)$$ $$e\left(\frac{409}{462}\right)$$ $$e\left(\frac{71}{462}\right)$$ $$e\left(\frac{195}{308}\right)$$ $$e\left(\frac{235}{308}\right)$$ $$e\left(\frac{157}{924}\right)$$ $$e\left(\frac{61}{462}\right)$$ $$e\left(\frac{29}{924}\right)$$ $$e\left(\frac{118}{231}\right)$$
$$\chi_{6003}(13,\cdot)$$ 6003.dk 462 yes $$1$$ $$1$$ $$e\left(\frac{115}{462}\right)$$ $$e\left(\frac{115}{231}\right)$$ $$e\left(\frac{103}{231}\right)$$ $$e\left(\frac{32}{231}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{107}{154}\right)$$ $$e\left(\frac{61}{462}\right)$$ $$e\left(\frac{34}{231}\right)$$ $$e\left(\frac{179}{462}\right)$$ $$e\left(\frac{230}{231}\right)$$
$$\chi_{6003}(14,\cdot)$$ 6003.dr 924 yes $$-1$$ $$1$$ $$e\left(\frac{191}{924}\right)$$ $$e\left(\frac{191}{462}\right)$$ $$e\left(\frac{155}{462}\right)$$ $$e\left(\frac{19}{462}\right)$$ $$e\left(\frac{191}{308}\right)$$ $$e\left(\frac{167}{308}\right)$$ $$e\left(\frac{29}{924}\right)$$ $$e\left(\frac{179}{462}\right)$$ $$e\left(\frac{229}{924}\right)$$ $$e\left(\frac{191}{231}\right)$$
$$\chi_{6003}(16,\cdot)$$ 6003.dc 231 yes $$1$$ $$1$$ $$e\left(\frac{124}{231}\right)$$ $$e\left(\frac{17}{231}\right)$$ $$e\left(\frac{194}{231}\right)$$ $$e\left(\frac{67}{231}\right)$$ $$e\left(\frac{47}{77}\right)$$ $$e\left(\frac{29}{77}\right)$$ $$e\left(\frac{118}{231}\right)$$ $$e\left(\frac{230}{231}\right)$$ $$e\left(\frac{191}{231}\right)$$ $$e\left(\frac{34}{231}\right)$$
$$\chi_{6003}(17,\cdot)$$ 6003.ce 44 no $$-1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{6003}(19,\cdot)$$ 6003.df 308 no $$1$$ $$1$$ $$e\left(\frac{211}{308}\right)$$ $$e\left(\frac{57}{154}\right)$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{125}{154}\right)$$ $$e\left(\frac{17}{308}\right)$$ $$e\left(\frac{135}{308}\right)$$ $$e\left(\frac{53}{308}\right)$$ $$e\left(\frac{51}{154}\right)$$ $$e\left(\frac{153}{308}\right)$$ $$e\left(\frac{57}{77}\right)$$
$$\chi_{6003}(20,\cdot)$$ 6003.dl 462 yes $$1$$ $$1$$ $$e\left(\frac{221}{462}\right)$$ $$e\left(\frac{221}{231}\right)$$ $$e\left(\frac{212}{231}\right)$$ $$e\left(\frac{125}{462}\right)$$ $$e\left(\frac{67}{154}\right)$$ $$e\left(\frac{61}{154}\right)$$ $$e\left(\frac{148}{231}\right)$$ $$e\left(\frac{218}{231}\right)$$ $$e\left(\frac{173}{231}\right)$$ $$e\left(\frac{211}{231}\right)$$
$$\chi_{6003}(22,\cdot)$$ 6003.bu 42 yes $$-1$$ $$1$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{21}\right)$$
$$\chi_{6003}(25,\cdot)$$ 6003.dc 231 yes $$1$$ $$1$$ $$e\left(\frac{97}{231}\right)$$ $$e\left(\frac{194}{231}\right)$$ $$e\left(\frac{230}{231}\right)$$ $$e\left(\frac{58}{231}\right)$$ $$e\left(\frac{20}{77}\right)$$ $$e\left(\frac{32}{77}\right)$$ $$e\left(\frac{178}{231}\right)$$ $$e\left(\frac{206}{231}\right)$$ $$e\left(\frac{155}{231}\right)$$ $$e\left(\frac{157}{231}\right)$$
$$\chi_{6003}(26,\cdot)$$ 6003.dg 308 no $$1$$ $$1$$ $$e\left(\frac{195}{308}\right)$$ $$e\left(\frac{41}{154}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{74}{77}\right)$$ $$e\left(\frac{277}{308}\right)$$ $$e\left(\frac{243}{308}\right)$$ $$e\left(\frac{3}{308}\right)$$ $$e\left(\frac{61}{154}\right)$$ $$e\left(\frac{183}{308}\right)$$ $$e\left(\frac{41}{77}\right)$$
$$\chi_{6003}(28,\cdot)$$ 6003.bo 22 no $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{6003}(31,\cdot)$$ 6003.dq 924 yes $$-1$$ $$1$$ $$e\left(\frac{845}{924}\right)$$ $$e\left(\frac{383}{462}\right)$$ $$e\left(\frac{335}{462}\right)$$ $$e\left(\frac{218}{231}\right)$$ $$e\left(\frac{229}{308}\right)$$ $$e\left(\frac{197}{308}\right)$$ $$e\left(\frac{629}{924}\right)$$ $$e\left(\frac{59}{462}\right)$$ $$e\left(\frac{793}{924}\right)$$ $$e\left(\frac{152}{231}\right)$$
$$\chi_{6003}(32,\cdot)$$ 6003.do 924 yes $$1$$ $$1$$ $$e\left(\frac{851}{924}\right)$$ $$e\left(\frac{389}{462}\right)$$ $$e\left(\frac{127}{231}\right)$$ $$e\left(\frac{26}{231}\right)$$ $$e\left(\frac{235}{308}\right)$$ $$e\left(\frac{145}{308}\right)$$ $$e\left(\frac{359}{924}\right)$$ $$e\left(\frac{113}{462}\right)$$ $$e\left(\frac{31}{924}\right)$$ $$e\left(\frac{158}{231}\right)$$
$$\chi_{6003}(34,\cdot)$$ 6003.dn 462 yes $$-1$$ $$1$$ $$e\left(\frac{125}{462}\right)$$ $$e\left(\frac{125}{231}\right)$$ $$e\left(\frac{13}{462}\right)$$ $$e\left(\frac{401}{462}\right)$$ $$e\left(\frac{125}{154}\right)$$ $$e\left(\frac{23}{77}\right)$$ $$e\left(\frac{229}{231}\right)$$ $$e\left(\frac{47}{231}\right)$$ $$e\left(\frac{32}{231}\right)$$ $$e\left(\frac{19}{231}\right)$$
$$\chi_{6003}(35,\cdot)$$ 6003.da 154 no $$-1$$ $$1$$ $$e\left(\frac{41}{77}\right)$$ $$e\left(\frac{5}{77}\right)$$ $$e\left(\frac{19}{154}\right)$$ $$e\left(\frac{65}{77}\right)$$ $$e\left(\frac{46}{77}\right)$$ $$e\left(\frac{101}{154}\right)$$ $$e\left(\frac{3}{77}\right)$$ $$e\left(\frac{45}{77}\right)$$ $$e\left(\frac{29}{77}\right)$$ $$e\left(\frac{10}{77}\right)$$
$$\chi_{6003}(37,\cdot)$$ 6003.df 308 no $$1$$ $$1$$ $$e\left(\frac{5}{308}\right)$$ $$e\left(\frac{5}{154}\right)$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{15}{308}\right)$$ $$e\left(\frac{101}{308}\right)$$ $$e\left(\frac{83}{308}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{135}{308}\right)$$ $$e\left(\frac{5}{77}\right)$$
$$\chi_{6003}(38,\cdot)$$ 6003.dh 462 yes $$1$$ $$1$$ $$e\left(\frac{16}{231}\right)$$ $$e\left(\frac{32}{231}\right)$$ $$e\left(\frac{107}{231}\right)$$ $$e\left(\frac{293}{462}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{41}{77}\right)$$ $$e\left(\frac{23}{462}\right)$$ $$e\left(\frac{134}{231}\right)$$ $$e\left(\frac{325}{462}\right)$$ $$e\left(\frac{64}{231}\right)$$
$$\chi_{6003}(40,\cdot)$$ 6003.dp 924 yes $$1$$ $$1$$ $$e\left(\frac{797}{924}\right)$$ $$e\left(\frac{335}{462}\right)$$ $$e\left(\frac{145}{231}\right)$$ $$e\left(\frac{43}{462}\right)$$ $$e\left(\frac{181}{308}\right)$$ $$e\left(\frac{151}{308}\right)$$ $$e\left(\frac{479}{924}\right)$$ $$e\left(\frac{89}{462}\right)$$ $$e\left(\frac{883}{924}\right)$$ $$e\left(\frac{104}{231}\right)$$
$$\chi_{6003}(41,\cdot)$$ 6003.cu 132 yes $$1$$ $$1$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{115}{132}\right)$$ $$e\left(\frac{23}{33}\right)$$
$$\chi_{6003}(43,\cdot)$$ 6003.dp 924 yes $$1$$ $$1$$ $$e\left(\frac{541}{924}\right)$$ $$e\left(\frac{79}{462}\right)$$ $$e\left(\frac{179}{231}\right)$$ $$e\left(\frac{257}{462}\right)$$ $$e\left(\frac{233}{308}\right)$$ $$e\left(\frac{111}{308}\right)$$ $$e\left(\frac{295}{924}\right)$$ $$e\left(\frac{403}{462}\right)$$ $$e\left(\frac{131}{924}\right)$$ $$e\left(\frac{79}{231}\right)$$
$$\chi_{6003}(44,\cdot)$$ 6003.dd 308 no $$-1$$ $$1$$ $$e\left(\frac{199}{308}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{123}{154}\right)$$ $$e\left(\frac{289}{308}\right)$$ $$e\left(\frac{293}{308}\right)$$ $$e\left(\frac{285}{308}\right)$$ $$e\left(\frac{97}{154}\right)$$ $$e\left(\frac{137}{308}\right)$$ $$e\left(\frac{45}{77}\right)$$
$$\chi_{6003}(47,\cdot)$$ 6003.cq 84 no $$1$$ $$1$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{83}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{79}{84}\right)$$ $$e\left(\frac{5}{21}\right)$$
$$\chi_{6003}(49,\cdot)$$ 6003.dc 231 yes $$1$$ $$1$$ $$e\left(\frac{149}{231}\right)$$ $$e\left(\frac{67}{231}\right)$$ $$e\left(\frac{58}{231}\right)$$ $$e\left(\frac{101}{231}\right)$$ $$e\left(\frac{72}{77}\right)$$ $$e\left(\frac{69}{77}\right)$$ $$e\left(\frac{71}{231}\right)$$ $$e\left(\frac{64}{231}\right)$$ $$e\left(\frac{19}{231}\right)$$ $$e\left(\frac{134}{231}\right)$$
$$\chi_{6003}(50,\cdot)$$ 6003.do 924 yes $$1$$ $$1$$ $$e\left(\frac{743}{924}\right)$$ $$e\left(\frac{281}{462}\right)$$ $$e\left(\frac{163}{231}\right)$$ $$e\left(\frac{17}{231}\right)$$ $$e\left(\frac{127}{308}\right)$$ $$e\left(\frac{157}{308}\right)$$ $$e\left(\frac{599}{924}\right)$$ $$e\left(\frac{65}{462}\right)$$ $$e\left(\frac{811}{924}\right)$$ $$e\left(\frac{50}{231}\right)$$
$$\chi_{6003}(52,\cdot)$$ 6003.dc 231 yes $$1$$ $$1$$ $$e\left(\frac{4}{231}\right)$$ $$e\left(\frac{8}{231}\right)$$ $$e\left(\frac{200}{231}\right)$$ $$e\left(\frac{181}{231}\right)$$ $$e\left(\frac{4}{77}\right)$$ $$e\left(\frac{68}{77}\right)$$ $$e\left(\frac{205}{231}\right)$$ $$e\left(\frac{149}{231}\right)$$ $$e\left(\frac{185}{231}\right)$$ $$e\left(\frac{16}{231}\right)$$