# Properties

 Modulus 4022 Structure $$C_{2010}$$ Order 2010

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4022)

pari: g = idealstar(,4022,2)

## Character group

 sage: G.order()  pari: g.no Order = 2010 sage: H.invariants()  pari: g.cyc Structure = $$C_{2010}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4022}(3,\cdot)$

## First 32 of 2010 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 3 5 7 9 11 13 15 17 19 21
$$\chi_{4022}(1,\cdot)$$ 4022.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4022}(3,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{1}{2010}\right)$$ $$e\left(\frac{512}{1005}\right)$$ $$e\left(\frac{1807}{2010}\right)$$ $$e\left(\frac{1}{1005}\right)$$ $$e\left(\frac{1037}{2010}\right)$$ $$e\left(\frac{323}{335}\right)$$ $$e\left(\frac{205}{402}\right)$$ $$e\left(\frac{347}{2010}\right)$$ $$e\left(\frac{1163}{2010}\right)$$ $$e\left(\frac{904}{1005}\right)$$
$$\chi_{4022}(5,\cdot)$$ 4022.o 1005 no $$1$$ $$1$$ $$e\left(\frac{512}{1005}\right)$$ $$e\left(\frac{683}{1005}\right)$$ $$e\left(\frac{584}{1005}\right)$$ $$e\left(\frac{19}{1005}\right)$$ $$e\left(\frac{304}{1005}\right)$$ $$e\left(\frac{107}{335}\right)$$ $$e\left(\frac{38}{201}\right)$$ $$e\left(\frac{784}{1005}\right)$$ $$e\left(\frac{496}{1005}\right)$$ $$e\left(\frac{91}{1005}\right)$$
$$\chi_{4022}(7,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{1807}{2010}\right)$$ $$e\left(\frac{584}{1005}\right)$$ $$e\left(\frac{1009}{2010}\right)$$ $$e\left(\frac{802}{1005}\right)$$ $$e\left(\frac{539}{2010}\right)$$ $$e\left(\frac{91}{335}\right)$$ $$e\left(\frac{193}{402}\right)$$ $$e\left(\frac{1919}{2010}\right)$$ $$e\left(\frac{1091}{2010}\right)$$ $$e\left(\frac{403}{1005}\right)$$
$$\chi_{4022}(9,\cdot)$$ 4022.o 1005 no $$1$$ $$1$$ $$e\left(\frac{1}{1005}\right)$$ $$e\left(\frac{19}{1005}\right)$$ $$e\left(\frac{802}{1005}\right)$$ $$e\left(\frac{2}{1005}\right)$$ $$e\left(\frac{32}{1005}\right)$$ $$e\left(\frac{311}{335}\right)$$ $$e\left(\frac{4}{201}\right)$$ $$e\left(\frac{347}{1005}\right)$$ $$e\left(\frac{158}{1005}\right)$$ $$e\left(\frac{803}{1005}\right)$$
$$\chi_{4022}(11,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{1037}{2010}\right)$$ $$e\left(\frac{304}{1005}\right)$$ $$e\left(\frac{539}{2010}\right)$$ $$e\left(\frac{32}{1005}\right)$$ $$e\left(\frac{19}{2010}\right)$$ $$e\left(\frac{286}{335}\right)$$ $$e\left(\frac{329}{402}\right)$$ $$e\left(\frac{49}{2010}\right)$$ $$e\left(\frac{31}{2010}\right)$$ $$e\left(\frac{788}{1005}\right)$$
$$\chi_{4022}(13,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{323}{335}\right)$$ $$e\left(\frac{107}{335}\right)$$ $$e\left(\frac{91}{335}\right)$$ $$e\left(\frac{311}{335}\right)$$ $$e\left(\frac{286}{335}\right)$$ $$e\left(\frac{194}{335}\right)$$ $$e\left(\frac{19}{67}\right)$$ $$e\left(\frac{191}{335}\right)$$ $$e\left(\frac{114}{335}\right)$$ $$e\left(\frac{79}{335}\right)$$
$$\chi_{4022}(15,\cdot)$$ 4022.m 402 no $$-1$$ $$1$$ $$e\left(\frac{205}{402}\right)$$ $$e\left(\frac{38}{201}\right)$$ $$e\left(\frac{193}{402}\right)$$ $$e\left(\frac{4}{201}\right)$$ $$e\left(\frac{329}{402}\right)$$ $$e\left(\frac{19}{67}\right)$$ $$e\left(\frac{281}{402}\right)$$ $$e\left(\frac{383}{402}\right)$$ $$e\left(\frac{29}{402}\right)$$ $$e\left(\frac{199}{201}\right)$$
$$\chi_{4022}(17,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{347}{2010}\right)$$ $$e\left(\frac{784}{1005}\right)$$ $$e\left(\frac{1919}{2010}\right)$$ $$e\left(\frac{347}{1005}\right)$$ $$e\left(\frac{49}{2010}\right)$$ $$e\left(\frac{191}{335}\right)$$ $$e\left(\frac{383}{402}\right)$$ $$e\left(\frac{1819}{2010}\right)$$ $$e\left(\frac{1561}{2010}\right)$$ $$e\left(\frac{128}{1005}\right)$$
$$\chi_{4022}(19,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{1163}{2010}\right)$$ $$e\left(\frac{496}{1005}\right)$$ $$e\left(\frac{1091}{2010}\right)$$ $$e\left(\frac{158}{1005}\right)$$ $$e\left(\frac{31}{2010}\right)$$ $$e\left(\frac{114}{335}\right)$$ $$e\left(\frac{29}{402}\right)$$ $$e\left(\frac{1561}{2010}\right)$$ $$e\left(\frac{1849}{2010}\right)$$ $$e\left(\frac{122}{1005}\right)$$
$$\chi_{4022}(21,\cdot)$$ 4022.o 1005 no $$1$$ $$1$$ $$e\left(\frac{904}{1005}\right)$$ $$e\left(\frac{91}{1005}\right)$$ $$e\left(\frac{403}{1005}\right)$$ $$e\left(\frac{803}{1005}\right)$$ $$e\left(\frac{788}{1005}\right)$$ $$e\left(\frac{79}{335}\right)$$ $$e\left(\frac{199}{201}\right)$$ $$e\left(\frac{128}{1005}\right)$$ $$e\left(\frac{122}{1005}\right)$$ $$e\left(\frac{302}{1005}\right)$$
$$\chi_{4022}(23,\cdot)$$ 4022.o 1005 no $$1$$ $$1$$ $$e\left(\frac{83}{1005}\right)$$ $$e\left(\frac{572}{1005}\right)$$ $$e\left(\frac{236}{1005}\right)$$ $$e\left(\frac{166}{1005}\right)$$ $$e\left(\frac{646}{1005}\right)$$ $$e\left(\frac{18}{335}\right)$$ $$e\left(\frac{131}{201}\right)$$ $$e\left(\frac{661}{1005}\right)$$ $$e\left(\frac{49}{1005}\right)$$ $$e\left(\frac{319}{1005}\right)$$
$$\chi_{4022}(25,\cdot)$$ 4022.o 1005 no $$1$$ $$1$$ $$e\left(\frac{19}{1005}\right)$$ $$e\left(\frac{361}{1005}\right)$$ $$e\left(\frac{163}{1005}\right)$$ $$e\left(\frac{38}{1005}\right)$$ $$e\left(\frac{608}{1005}\right)$$ $$e\left(\frac{214}{335}\right)$$ $$e\left(\frac{76}{201}\right)$$ $$e\left(\frac{563}{1005}\right)$$ $$e\left(\frac{992}{1005}\right)$$ $$e\left(\frac{182}{1005}\right)$$
$$\chi_{4022}(27,\cdot)$$ 4022.n 670 no $$-1$$ $$1$$ $$e\left(\frac{1}{670}\right)$$ $$e\left(\frac{177}{335}\right)$$ $$e\left(\frac{467}{670}\right)$$ $$e\left(\frac{1}{335}\right)$$ $$e\left(\frac{367}{670}\right)$$ $$e\left(\frac{299}{335}\right)$$ $$e\left(\frac{71}{134}\right)$$ $$e\left(\frac{347}{670}\right)$$ $$e\left(\frac{493}{670}\right)$$ $$e\left(\frac{234}{335}\right)$$
$$\chi_{4022}(29,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{97}{2010}\right)$$ $$e\left(\frac{419}{1005}\right)$$ $$e\left(\frac{409}{2010}\right)$$ $$e\left(\frac{97}{1005}\right)$$ $$e\left(\frac{89}{2010}\right)$$ $$e\left(\frac{176}{335}\right)$$ $$e\left(\frac{187}{402}\right)$$ $$e\left(\frac{1499}{2010}\right)$$ $$e\left(\frac{251}{2010}\right)$$ $$e\left(\frac{253}{1005}\right)$$
$$\chi_{4022}(31,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{258}{335}\right)$$ $$e\left(\frac{212}{335}\right)$$ $$e\left(\frac{221}{335}\right)$$ $$e\left(\frac{181}{335}\right)$$ $$e\left(\frac{216}{335}\right)$$ $$e\left(\frac{184}{335}\right)$$ $$e\left(\frac{27}{67}\right)$$ $$e\left(\frac{81}{335}\right)$$ $$e\left(\frac{229}{335}\right)$$ $$e\left(\frac{144}{335}\right)$$
$$\chi_{4022}(33,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{173}{335}\right)$$ $$e\left(\frac{272}{335}\right)$$ $$e\left(\frac{56}{335}\right)$$ $$e\left(\frac{11}{335}\right)$$ $$e\left(\frac{176}{335}\right)$$ $$e\left(\frac{274}{335}\right)$$ $$e\left(\frac{22}{67}\right)$$ $$e\left(\frac{66}{335}\right)$$ $$e\left(\frac{199}{335}\right)$$ $$e\left(\frac{229}{335}\right)$$
$$\chi_{4022}(35,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{821}{2010}\right)$$ $$e\left(\frac{262}{1005}\right)$$ $$e\left(\frac{167}{2010}\right)$$ $$e\left(\frac{821}{1005}\right)$$ $$e\left(\frac{1147}{2010}\right)$$ $$e\left(\frac{198}{335}\right)$$ $$e\left(\frac{269}{402}\right)$$ $$e\left(\frac{1477}{2010}\right)$$ $$e\left(\frac{73}{2010}\right)$$ $$e\left(\frac{494}{1005}\right)$$
$$\chi_{4022}(37,\cdot)$$ 4022.m 402 no $$-1$$ $$1$$ $$e\left(\frac{137}{402}\right)$$ $$e\left(\frac{196}{201}\right)$$ $$e\left(\frac{329}{402}\right)$$ $$e\left(\frac{137}{201}\right)$$ $$e\left(\frac{163}{402}\right)$$ $$e\left(\frac{31}{67}\right)$$ $$e\left(\frac{127}{402}\right)$$ $$e\left(\frac{103}{402}\right)$$ $$e\left(\frac{139}{402}\right)$$ $$e\left(\frac{32}{201}\right)$$
$$\chi_{4022}(39,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{1939}{2010}\right)$$ $$e\left(\frac{833}{1005}\right)$$ $$e\left(\frac{343}{2010}\right)$$ $$e\left(\frac{934}{1005}\right)$$ $$e\left(\frac{743}{2010}\right)$$ $$e\left(\frac{182}{335}\right)$$ $$e\left(\frac{319}{402}\right)$$ $$e\left(\frac{1493}{2010}\right)$$ $$e\left(\frac{1847}{2010}\right)$$ $$e\left(\frac{136}{1005}\right)$$
$$\chi_{4022}(41,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{276}{335}\right)$$ $$e\left(\frac{219}{335}\right)$$ $$e\left(\frac{252}{335}\right)$$ $$e\left(\frac{217}{335}\right)$$ $$e\left(\frac{122}{335}\right)$$ $$e\left(\frac{228}{335}\right)$$ $$e\left(\frac{32}{67}\right)$$ $$e\left(\frac{297}{335}\right)$$ $$e\left(\frac{58}{335}\right)$$ $$e\left(\frac{193}{335}\right)$$
$$\chi_{4022}(43,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{272}{335}\right)$$ $$e\left(\frac{143}{335}\right)$$ $$e\left(\frac{59}{335}\right)$$ $$e\left(\frac{209}{335}\right)$$ $$e\left(\frac{329}{335}\right)$$ $$e\left(\frac{181}{335}\right)$$ $$e\left(\frac{16}{67}\right)$$ $$e\left(\frac{249}{335}\right)$$ $$e\left(\frac{96}{335}\right)$$ $$e\left(\frac{331}{335}\right)$$
$$\chi_{4022}(45,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{171}{335}\right)$$ $$e\left(\frac{234}{335}\right)$$ $$e\left(\frac{127}{335}\right)$$ $$e\left(\frac{7}{335}\right)$$ $$e\left(\frac{112}{335}\right)$$ $$e\left(\frac{83}{335}\right)$$ $$e\left(\frac{14}{67}\right)$$ $$e\left(\frac{42}{335}\right)$$ $$e\left(\frac{218}{335}\right)$$ $$e\left(\frac{298}{335}\right)$$
$$\chi_{4022}(47,\cdot)$$ 4022.n 670 no $$-1$$ $$1$$ $$e\left(\frac{549}{670}\right)$$ $$e\left(\frac{23}{335}\right)$$ $$e\left(\frac{443}{670}\right)$$ $$e\left(\frac{214}{335}\right)$$ $$e\left(\frac{483}{670}\right)$$ $$e\left(\frac{1}{335}\right)$$ $$e\left(\frac{119}{134}\right)$$ $$e\left(\frac{223}{670}\right)$$ $$e\left(\frac{647}{670}\right)$$ $$e\left(\frac{161}{335}\right)$$
$$\chi_{4022}(49,\cdot)$$ 4022.o 1005 no $$1$$ $$1$$ $$e\left(\frac{802}{1005}\right)$$ $$e\left(\frac{163}{1005}\right)$$ $$e\left(\frac{4}{1005}\right)$$ $$e\left(\frac{599}{1005}\right)$$ $$e\left(\frac{539}{1005}\right)$$ $$e\left(\frac{182}{335}\right)$$ $$e\left(\frac{193}{201}\right)$$ $$e\left(\frac{914}{1005}\right)$$ $$e\left(\frac{86}{1005}\right)$$ $$e\left(\frac{806}{1005}\right)$$
$$\chi_{4022}(51,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{58}{335}\right)$$ $$e\left(\frac{97}{335}\right)$$ $$e\left(\frac{286}{335}\right)$$ $$e\left(\frac{116}{335}\right)$$ $$e\left(\frac{181}{335}\right)$$ $$e\left(\frac{179}{335}\right)$$ $$e\left(\frac{31}{67}\right)$$ $$e\left(\frac{26}{335}\right)$$ $$e\left(\frac{119}{335}\right)$$ $$e\left(\frac{9}{335}\right)$$
$$\chi_{4022}(53,\cdot)$$ 4022.f 10 no $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{4022}(55,\cdot)$$ 4022.n 670 no $$-1$$ $$1$$ $$e\left(\frac{17}{670}\right)$$ $$e\left(\frac{329}{335}\right)$$ $$e\left(\frac{569}{670}\right)$$ $$e\left(\frac{17}{335}\right)$$ $$e\left(\frac{209}{670}\right)$$ $$e\left(\frac{58}{335}\right)$$ $$e\left(\frac{1}{134}\right)$$ $$e\left(\frac{539}{670}\right)$$ $$e\left(\frac{341}{670}\right)$$ $$e\left(\frac{293}{335}\right)$$
$$\chi_{4022}(57,\cdot)$$ 4022.l 335 no $$1$$ $$1$$ $$e\left(\frac{194}{335}\right)$$ $$e\left(\frac{1}{335}\right)$$ $$e\left(\frac{148}{335}\right)$$ $$e\left(\frac{53}{335}\right)$$ $$e\left(\frac{178}{335}\right)$$ $$e\left(\frac{102}{335}\right)$$ $$e\left(\frac{39}{67}\right)$$ $$e\left(\frac{318}{335}\right)$$ $$e\left(\frac{167}{335}\right)$$ $$e\left(\frac{7}{335}\right)$$
$$\chi_{4022}(59,\cdot)$$ 4022.n 670 no $$-1$$ $$1$$ $$e\left(\frac{479}{670}\right)$$ $$e\left(\frac{28}{335}\right)$$ $$e\left(\frac{583}{670}\right)$$ $$e\left(\frac{144}{335}\right)$$ $$e\left(\frac{253}{670}\right)$$ $$e\left(\frac{176}{335}\right)$$ $$e\left(\frac{107}{134}\right)$$ $$e\left(\frac{53}{670}\right)$$ $$e\left(\frac{307}{670}\right)$$ $$e\left(\frac{196}{335}\right)$$
$$\chi_{4022}(61,\cdot)$$ 4022.p 2010 no $$-1$$ $$1$$ $$e\left(\frac{1217}{2010}\right)$$ $$e\left(\frac{4}{1005}\right)$$ $$e\left(\frac{179}{2010}\right)$$ $$e\left(\frac{212}{1005}\right)$$ $$e\left(\frac{1759}{2010}\right)$$ $$e\left(\frac{136}{335}\right)$$ $$e\left(\frac{245}{402}\right)$$ $$e\left(\frac{199}{2010}\right)$$ $$e\left(\frac{331}{2010}\right)$$ $$e\left(\frac{698}{1005}\right)$$
$$\chi_{4022}(63,\cdot)$$ 4022.f 10 no $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$