# Properties

 Modulus $2001$ Structure $$C_{308}\times C_{2}\times C_{2}$$ Order $1232$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2001)

pari: g = idealstar(,2001,2)

## Character group

 sage: G.order()  pari: g.no Order = 1232 sage: H.invariants()  pari: g.cyc Structure = $$C_{308}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{2001}(668,\cdot)$, $\chi_{2001}(1132,\cdot)$, $\chi_{2001}(553,\cdot)$

## First 32 of 1232 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{2001}(1,\cdot)$$ 2001.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{2001}(2,\cdot)$$ 2001.bv 308 yes $$1$$ $$1$$ $$e\left(\frac{221}{308}\right)$$ $$e\left(\frac{67}{154}\right)$$ $$e\left(\frac{29}{77}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{47}{308}\right)$$ $$e\left(\frac{29}{308}\right)$$ $$e\left(\frac{65}{308}\right)$$ $$e\left(\frac{141}{154}\right)$$ $$e\left(\frac{269}{308}\right)$$ $$e\left(\frac{67}{77}\right)$$
$$\chi_{2001}(4,\cdot)$$ 2001.bo 154 no $$1$$ $$1$$ $$e\left(\frac{67}{154}\right)$$ $$e\left(\frac{67}{77}\right)$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{29}{154}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{64}{77}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{57}{77}\right)$$
$$\chi_{2001}(5,\cdot)$$ 2001.br 154 yes $$1$$ $$1$$ $$e\left(\frac{29}{77}\right)$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{64}{77}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{10}{77}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{85}{154}\right)$$ $$e\left(\frac{60}{77}\right)$$ $$e\left(\frac{103}{154}\right)$$ $$e\left(\frac{39}{77}\right)$$
$$\chi_{2001}(7,\cdot)$$ 2001.bp 154 no $$-1$$ $$1$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{85}{154}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{69}{154}\right)$$ $$e\left(\frac{75}{154}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{109}{154}\right)$$ $$e\left(\frac{48}{77}\right)$$
$$\chi_{2001}(8,\cdot)$$ 2001.bv 308 yes $$1$$ $$1$$ $$e\left(\frac{47}{308}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{10}{77}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{141}{308}\right)$$ $$e\left(\frac{87}{308}\right)$$ $$e\left(\frac{195}{308}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{191}{308}\right)$$ $$e\left(\frac{47}{77}\right)$$
$$\chi_{2001}(10,\cdot)$$ 2001.bu 308 no $$1$$ $$1$$ $$e\left(\frac{29}{308}\right)$$ $$e\left(\frac{29}{154}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{69}{154}\right)$$ $$e\left(\frac{87}{308}\right)$$ $$e\left(\frac{93}{308}\right)$$ $$e\left(\frac{235}{308}\right)$$ $$e\left(\frac{107}{154}\right)$$ $$e\left(\frac{167}{308}\right)$$ $$e\left(\frac{29}{77}\right)$$
$$\chi_{2001}(11,\cdot)$$ 2001.bs 308 yes $$-1$$ $$1$$ $$e\left(\frac{65}{308}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{85}{154}\right)$$ $$e\left(\frac{75}{154}\right)$$ $$e\left(\frac{195}{308}\right)$$ $$e\left(\frac{235}{308}\right)$$ $$e\left(\frac{155}{308}\right)$$ $$e\left(\frac{123}{154}\right)$$ $$e\left(\frac{215}{308}\right)$$ $$e\left(\frac{65}{77}\right)$$
$$\chi_{2001}(13,\cdot)$$ 2001.bo 154 no $$1$$ $$1$$ $$e\left(\frac{141}{154}\right)$$ $$e\left(\frac{64}{77}\right)$$ $$e\left(\frac{60}{77}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{107}{154}\right)$$ $$e\left(\frac{123}{154}\right)$$ $$e\left(\frac{37}{77}\right)$$ $$e\left(\frac{111}{154}\right)$$ $$e\left(\frac{51}{77}\right)$$
$$\chi_{2001}(14,\cdot)$$ 2001.bs 308 yes $$-1$$ $$1$$ $$e\left(\frac{269}{308}\right)$$ $$e\left(\frac{115}{154}\right)$$ $$e\left(\frac{103}{154}\right)$$ $$e\left(\frac{109}{154}\right)$$ $$e\left(\frac{191}{308}\right)$$ $$e\left(\frac{167}{308}\right)$$ $$e\left(\frac{215}{308}\right)$$ $$e\left(\frac{111}{154}\right)$$ $$e\left(\frac{179}{308}\right)$$ $$e\left(\frac{38}{77}\right)$$
$$\chi_{2001}(16,\cdot)$$ 2001.bk 77 no $$1$$ $$1$$ $$e\left(\frac{67}{77}\right)$$ $$e\left(\frac{57}{77}\right)$$ $$e\left(\frac{39}{77}\right)$$ $$e\left(\frac{48}{77}\right)$$ $$e\left(\frac{47}{77}\right)$$ $$e\left(\frac{29}{77}\right)$$ $$e\left(\frac{65}{77}\right)$$ $$e\left(\frac{51}{77}\right)$$ $$e\left(\frac{38}{77}\right)$$ $$e\left(\frac{37}{77}\right)$$
$$\chi_{2001}(17,\cdot)$$ 2001.bj 44 yes $$-1$$ $$1$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{2001}(19,\cdot)$$ 2001.bu 308 no $$1$$ $$1$$ $$e\left(\frac{211}{308}\right)$$ $$e\left(\frac{57}{154}\right)$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{125}{154}\right)$$ $$e\left(\frac{17}{308}\right)$$ $$e\left(\frac{135}{308}\right)$$ $$e\left(\frac{53}{308}\right)$$ $$e\left(\frac{51}{154}\right)$$ $$e\left(\frac{153}{308}\right)$$ $$e\left(\frac{57}{77}\right)$$
$$\chi_{2001}(20,\cdot)$$ 2001.bn 154 yes $$1$$ $$1$$ $$e\left(\frac{125}{154}\right)$$ $$e\left(\frac{48}{77}\right)$$ $$e\left(\frac{45}{77}\right)$$ $$e\left(\frac{93}{154}\right)$$ $$e\left(\frac{67}{154}\right)$$ $$e\left(\frac{61}{154}\right)$$ $$e\left(\frac{75}{77}\right)$$ $$e\left(\frac{47}{77}\right)$$ $$e\left(\frac{32}{77}\right)$$ $$e\left(\frac{19}{77}\right)$$
$$\chi_{2001}(22,\cdot)$$ 2001.u 14 no $$-1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{2001}(25,\cdot)$$ 2001.bk 77 no $$1$$ $$1$$ $$e\left(\frac{58}{77}\right)$$ $$e\left(\frac{39}{77}\right)$$ $$e\left(\frac{51}{77}\right)$$ $$e\left(\frac{45}{77}\right)$$ $$e\left(\frac{20}{77}\right)$$ $$e\left(\frac{32}{77}\right)$$ $$e\left(\frac{8}{77}\right)$$ $$e\left(\frac{43}{77}\right)$$ $$e\left(\frac{26}{77}\right)$$ $$e\left(\frac{1}{77}\right)$$
$$\chi_{2001}(26,\cdot)$$ 2001.bv 308 yes $$1$$ $$1$$ $$e\left(\frac{195}{308}\right)$$ $$e\left(\frac{41}{154}\right)$$ $$e\left(\frac{12}{77}\right)$$ $$e\left(\frac{74}{77}\right)$$ $$e\left(\frac{277}{308}\right)$$ $$e\left(\frac{243}{308}\right)$$ $$e\left(\frac{3}{308}\right)$$ $$e\left(\frac{61}{154}\right)$$ $$e\left(\frac{183}{308}\right)$$ $$e\left(\frac{41}{77}\right)$$
$$\chi_{2001}(28,\cdot)$$ 2001.bb 22 no $$-1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{2001}(31,\cdot)$$ 2001.bt 308 no $$-1$$ $$1$$ $$e\left(\frac{179}{308}\right)$$ $$e\left(\frac{25}{154}\right)$$ $$e\left(\frac{9}{154}\right)$$ $$e\left(\frac{47}{77}\right)$$ $$e\left(\frac{229}{308}\right)$$ $$e\left(\frac{197}{308}\right)$$ $$e\left(\frac{107}{308}\right)$$ $$e\left(\frac{71}{154}\right)$$ $$e\left(\frac{59}{308}\right)$$ $$e\left(\frac{25}{77}\right)$$
$$\chi_{2001}(32,\cdot)$$ 2001.bv 308 yes $$1$$ $$1$$ $$e\left(\frac{181}{308}\right)$$ $$e\left(\frac{27}{154}\right)$$ $$e\left(\frac{68}{77}\right)$$ $$e\left(\frac{60}{77}\right)$$ $$e\left(\frac{235}{308}\right)$$ $$e\left(\frac{145}{308}\right)$$ $$e\left(\frac{17}{308}\right)$$ $$e\left(\frac{89}{154}\right)$$ $$e\left(\frac{113}{308}\right)$$ $$e\left(\frac{27}{77}\right)$$
$$\chi_{2001}(34,\cdot)$$ 2001.bl 154 no $$-1$$ $$1$$ $$e\left(\frac{93}{154}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{107}{154}\right)$$ $$e\left(\frac{31}{154}\right)$$ $$e\left(\frac{125}{154}\right)$$ $$e\left(\frac{23}{77}\right)$$ $$e\left(\frac{25}{77}\right)$$ $$e\left(\frac{67}{77}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{32}{77}\right)$$
$$\chi_{2001}(35,\cdot)$$ 2001.bq 154 yes $$-1$$ $$1$$ $$e\left(\frac{41}{77}\right)$$ $$e\left(\frac{5}{77}\right)$$ $$e\left(\frac{19}{154}\right)$$ $$e\left(\frac{65}{77}\right)$$ $$e\left(\frac{46}{77}\right)$$ $$e\left(\frac{101}{154}\right)$$ $$e\left(\frac{3}{77}\right)$$ $$e\left(\frac{45}{77}\right)$$ $$e\left(\frac{29}{77}\right)$$ $$e\left(\frac{10}{77}\right)$$
$$\chi_{2001}(37,\cdot)$$ 2001.bu 308 no $$1$$ $$1$$ $$e\left(\frac{5}{308}\right)$$ $$e\left(\frac{5}{154}\right)$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{65}{154}\right)$$ $$e\left(\frac{15}{308}\right)$$ $$e\left(\frac{101}{308}\right)$$ $$e\left(\frac{83}{308}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{135}{308}\right)$$ $$e\left(\frac{5}{77}\right)$$
$$\chi_{2001}(38,\cdot)$$ 2001.br 154 yes $$1$$ $$1$$ $$e\left(\frac{31}{77}\right)$$ $$e\left(\frac{62}{77}\right)$$ $$e\left(\frac{10}{77}\right)$$ $$e\left(\frac{149}{154}\right)$$ $$e\left(\frac{16}{77}\right)$$ $$e\left(\frac{41}{77}\right)$$ $$e\left(\frac{59}{154}\right)$$ $$e\left(\frac{19}{77}\right)$$ $$e\left(\frac{57}{154}\right)$$ $$e\left(\frac{47}{77}\right)$$
$$\chi_{2001}(40,\cdot)$$ 2001.bu 308 no $$1$$ $$1$$ $$e\left(\frac{163}{308}\right)$$ $$e\left(\frac{9}{154}\right)$$ $$e\left(\frac{74}{77}\right)$$ $$e\left(\frac{117}{154}\right)$$ $$e\left(\frac{181}{308}\right)$$ $$e\left(\frac{151}{308}\right)$$ $$e\left(\frac{57}{308}\right)$$ $$e\left(\frac{81}{154}\right)$$ $$e\left(\frac{89}{308}\right)$$ $$e\left(\frac{9}{77}\right)$$
$$\chi_{2001}(41,\cdot)$$ 2001.bg 44 yes $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{2001}(43,\cdot)$$ 2001.bu 308 no $$1$$ $$1$$ $$e\left(\frac{283}{308}\right)$$ $$e\left(\frac{129}{154}\right)$$ $$e\left(\frac{34}{77}\right)$$ $$e\left(\frac{137}{154}\right)$$ $$e\left(\frac{233}{308}\right)$$ $$e\left(\frac{111}{308}\right)$$ $$e\left(\frac{201}{308}\right)$$ $$e\left(\frac{83}{154}\right)$$ $$e\left(\frac{249}{308}\right)$$ $$e\left(\frac{52}{77}\right)$$
$$\chi_{2001}(44,\cdot)$$ 2001.bs 308 yes $$-1$$ $$1$$ $$e\left(\frac{199}{308}\right)$$ $$e\left(\frac{45}{154}\right)$$ $$e\left(\frac{47}{154}\right)$$ $$e\left(\frac{123}{154}\right)$$ $$e\left(\frac{289}{308}\right)$$ $$e\left(\frac{293}{308}\right)$$ $$e\left(\frac{285}{308}\right)$$ $$e\left(\frac{97}{154}\right)$$ $$e\left(\frac{137}{308}\right)$$ $$e\left(\frac{45}{77}\right)$$
$$\chi_{2001}(47,\cdot)$$ 2001.bc 28 no $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{2001}(49,\cdot)$$ 2001.bk 77 no $$1$$ $$1$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{48}{77}\right)$$ $$e\left(\frac{45}{77}\right)$$ $$e\left(\frac{8}{77}\right)$$ $$e\left(\frac{72}{77}\right)$$ $$e\left(\frac{69}{77}\right)$$ $$e\left(\frac{75}{77}\right)$$ $$e\left(\frac{47}{77}\right)$$ $$e\left(\frac{32}{77}\right)$$ $$e\left(\frac{19}{77}\right)$$
$$\chi_{2001}(50,\cdot)$$ 2001.bv 308 yes $$1$$ $$1$$ $$e\left(\frac{145}{308}\right)$$ $$e\left(\frac{145}{154}\right)$$ $$e\left(\frac{3}{77}\right)$$ $$e\left(\frac{57}{77}\right)$$ $$e\left(\frac{127}{308}\right)$$ $$e\left(\frac{157}{308}\right)$$ $$e\left(\frac{97}{308}\right)$$ $$e\left(\frac{73}{154}\right)$$ $$e\left(\frac{65}{308}\right)$$ $$e\left(\frac{68}{77}\right)$$
$$\chi_{2001}(52,\cdot)$$ 2001.bk 77 no $$1$$ $$1$$ $$e\left(\frac{27}{77}\right)$$ $$e\left(\frac{54}{77}\right)$$ $$e\left(\frac{41}{77}\right)$$ $$e\left(\frac{9}{77}\right)$$ $$e\left(\frac{4}{77}\right)$$ $$e\left(\frac{68}{77}\right)$$ $$e\left(\frac{17}{77}\right)$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{36}{77}\right)$$ $$e\left(\frac{31}{77}\right)$$