# Properties

 Modulus 4016 Structure $$C_{500}\times C_{2}\times C_{2}$$ Order 2000

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4016)

pari: g = idealstar(,4016,2)

## Character group

 sage: G.order()  pari: g.no Order = 2000 sage: H.invariants()  pari: g.cyc Structure = $$C_{500}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4016}(1261,\cdot)$, $\chi_{4016}(1505,\cdot)$, $\chi_{4016}(2511,\cdot)$

## First 32 of 2000 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
$$\chi_{4016}(1,\cdot)$$ 4016.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4016}(3,\cdot)$$ 4016.bt 500 yes $$-1$$ $$1$$ $$e\left(\frac{387}{500}\right)$$ $$e\left(\frac{7}{100}\right)$$ $$e\left(\frac{109}{125}\right)$$ $$e\left(\frac{137}{250}\right)$$ $$e\left(\frac{377}{500}\right)$$ $$e\left(\frac{449}{500}\right)$$ $$e\left(\frac{211}{250}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{91}{500}\right)$$ $$e\left(\frac{323}{500}\right)$$
$$\chi_{4016}(5,\cdot)$$ 4016.bg 100 yes $$1$$ $$1$$ $$e\left(\frac{7}{100}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{97}{100}\right)$$ $$e\left(\frac{39}{100}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{53}{100}\right)$$
$$\chi_{4016}(7,\cdot)$$ 4016.bp 250 no $$-1$$ $$1$$ $$e\left(\frac{109}{125}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{129}{250}\right)$$ $$e\left(\frac{93}{125}\right)$$ $$e\left(\frac{39}{125}\right)$$ $$e\left(\frac{11}{250}\right)$$ $$e\left(\frac{83}{250}\right)$$ $$e\left(\frac{51}{125}\right)$$ $$e\left(\frac{87}{125}\right)$$ $$e\left(\frac{97}{250}\right)$$
$$\chi_{4016}(9,\cdot)$$ 4016.bq 250 no $$1$$ $$1$$ $$e\left(\frac{137}{250}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{93}{125}\right)$$ $$e\left(\frac{12}{125}\right)$$ $$e\left(\frac{127}{250}\right)$$ $$e\left(\frac{199}{250}\right)$$ $$e\left(\frac{86}{125}\right)$$ $$e\left(\frac{59}{125}\right)$$ $$e\left(\frac{91}{250}\right)$$ $$e\left(\frac{73}{250}\right)$$
$$\chi_{4016}(11,\cdot)$$ 4016.bv 500 yes $$1$$ $$1$$ $$e\left(\frac{377}{500}\right)$$ $$e\left(\frac{97}{100}\right)$$ $$e\left(\frac{39}{125}\right)$$ $$e\left(\frac{127}{250}\right)$$ $$e\left(\frac{417}{500}\right)$$ $$e\left(\frac{179}{500}\right)$$ $$e\left(\frac{181}{250}\right)$$ $$e\left(\frac{57}{125}\right)$$ $$e\left(\frac{411}{500}\right)$$ $$e\left(\frac{33}{500}\right)$$
$$\chi_{4016}(13,\cdot)$$ 4016.bu 500 yes $$1$$ $$1$$ $$e\left(\frac{449}{500}\right)$$ $$e\left(\frac{39}{100}\right)$$ $$e\left(\frac{11}{250}\right)$$ $$e\left(\frac{199}{250}\right)$$ $$e\left(\frac{179}{500}\right)$$ $$e\left(\frac{373}{500}\right)$$ $$e\left(\frac{36}{125}\right)$$ $$e\left(\frac{109}{125}\right)$$ $$e\left(\frac{457}{500}\right)$$ $$e\left(\frac{471}{500}\right)$$
$$\chi_{4016}(15,\cdot)$$ 4016.bn 250 no $$-1$$ $$1$$ $$e\left(\frac{211}{250}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{83}{250}\right)$$ $$e\left(\frac{86}{125}\right)$$ $$e\left(\frac{181}{250}\right)$$ $$e\left(\frac{36}{125}\right)$$ $$e\left(\frac{191}{250}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{173}{250}\right)$$ $$e\left(\frac{22}{125}\right)$$
$$\chi_{4016}(17,\cdot)$$ 4016.bk 125 no $$1$$ $$1$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{12}{25}\right)$$ $$e\left(\frac{51}{125}\right)$$ $$e\left(\frac{59}{125}\right)$$ $$e\left(\frac{57}{125}\right)$$ $$e\left(\frac{109}{125}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{113}{125}\right)$$ $$e\left(\frac{31}{125}\right)$$ $$e\left(\frac{18}{125}\right)$$
$$\chi_{4016}(19,\cdot)$$ 4016.bv 500 yes $$1$$ $$1$$ $$e\left(\frac{91}{500}\right)$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{87}{125}\right)$$ $$e\left(\frac{91}{250}\right)$$ $$e\left(\frac{411}{500}\right)$$ $$e\left(\frac{457}{500}\right)$$ $$e\left(\frac{173}{250}\right)$$ $$e\left(\frac{31}{125}\right)$$ $$e\left(\frac{13}{500}\right)$$ $$e\left(\frac{439}{500}\right)$$
$$\chi_{4016}(21,\cdot)$$ 4016.bu 500 yes $$1$$ $$1$$ $$e\left(\frac{323}{500}\right)$$ $$e\left(\frac{53}{100}\right)$$ $$e\left(\frac{97}{250}\right)$$ $$e\left(\frac{73}{250}\right)$$ $$e\left(\frac{33}{500}\right)$$ $$e\left(\frac{471}{500}\right)$$ $$e\left(\frac{22}{125}\right)$$ $$e\left(\frac{18}{125}\right)$$ $$e\left(\frac{439}{500}\right)$$ $$e\left(\frac{17}{500}\right)$$
$$\chi_{4016}(23,\cdot)$$ 4016.bp 250 no $$-1$$ $$1$$ $$e\left(\frac{67}{125}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{77}{250}\right)$$ $$e\left(\frac{9}{125}\right)$$ $$e\left(\frac{32}{125}\right)$$ $$e\left(\frac{243}{250}\right)$$ $$e\left(\frac{129}{250}\right)$$ $$e\left(\frac{13}{125}\right)$$ $$e\left(\frac{81}{125}\right)$$ $$e\left(\frac{211}{250}\right)$$
$$\chi_{4016}(25,\cdot)$$ 4016.bd 50 no $$1$$ $$1$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{3}{50}\right)$$
$$\chi_{4016}(27,\cdot)$$ 4016.bt 500 yes $$-1$$ $$1$$ $$e\left(\frac{161}{500}\right)$$ $$e\left(\frac{21}{100}\right)$$ $$e\left(\frac{77}{125}\right)$$ $$e\left(\frac{161}{250}\right)$$ $$e\left(\frac{131}{500}\right)$$ $$e\left(\frac{347}{500}\right)$$ $$e\left(\frac{133}{250}\right)$$ $$e\left(\frac{26}{125}\right)$$ $$e\left(\frac{273}{500}\right)$$ $$e\left(\frac{469}{500}\right)$$
$$\chi_{4016}(29,\cdot)$$ 4016.bs 500 yes $$-1$$ $$1$$ $$e\left(\frac{281}{500}\right)$$ $$e\left(\frac{91}{100}\right)$$ $$e\left(\frac{209}{250}\right)$$ $$e\left(\frac{31}{250}\right)$$ $$e\left(\frac{401}{500}\right)$$ $$e\left(\frac{337}{500}\right)$$ $$e\left(\frac{59}{125}\right)$$ $$e\left(\frac{71}{125}\right)$$ $$e\left(\frac{183}{500}\right)$$ $$e\left(\frac{199}{500}\right)$$
$$\chi_{4016}(31,\cdot)$$ 4016.bn 250 no $$-1$$ $$1$$ $$e\left(\frac{101}{250}\right)$$ $$e\left(\frac{18}{25}\right)$$ $$e\left(\frac{3}{250}\right)$$ $$e\left(\frac{101}{125}\right)$$ $$e\left(\frac{121}{250}\right)$$ $$e\left(\frac{51}{125}\right)$$ $$e\left(\frac{31}{250}\right)$$ $$e\left(\frac{7}{125}\right)$$ $$e\left(\frac{193}{250}\right)$$ $$e\left(\frac{52}{125}\right)$$
$$\chi_{4016}(33,\cdot)$$ 4016.bl 250 no $$-1$$ $$1$$ $$e\left(\frac{66}{125}\right)$$ $$e\left(\frac{1}{25}\right)$$ $$e\left(\frac{23}{125}\right)$$ $$e\left(\frac{7}{125}\right)$$ $$e\left(\frac{147}{250}\right)$$ $$e\left(\frac{32}{125}\right)$$ $$e\left(\frac{71}{125}\right)$$ $$e\left(\frac{24}{125}\right)$$ $$e\left(\frac{1}{250}\right)$$ $$e\left(\frac{89}{125}\right)$$
$$\chi_{4016}(35,\cdot)$$ 4016.bt 500 yes $$-1$$ $$1$$ $$e\left(\frac{471}{500}\right)$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{122}{125}\right)$$ $$e\left(\frac{221}{250}\right)$$ $$e\left(\frac{141}{500}\right)$$ $$e\left(\frac{217}{500}\right)$$ $$e\left(\frac{63}{250}\right)$$ $$e\left(\frac{111}{125}\right)$$ $$e\left(\frac{103}{500}\right)$$ $$e\left(\frac{459}{500}\right)$$
$$\chi_{4016}(37,\cdot)$$ 4016.bs 500 yes $$-1$$ $$1$$ $$e\left(\frac{499}{500}\right)$$ $$e\left(\frac{89}{100}\right)$$ $$e\left(\frac{211}{250}\right)$$ $$e\left(\frac{249}{250}\right)$$ $$e\left(\frac{479}{500}\right)$$ $$e\left(\frac{223}{500}\right)$$ $$e\left(\frac{111}{125}\right)$$ $$e\left(\frac{34}{125}\right)$$ $$e\left(\frac{357}{500}\right)$$ $$e\left(\frac{421}{500}\right)$$
$$\chi_{4016}(39,\cdot)$$ 4016.bp 250 no $$-1$$ $$1$$ $$e\left(\frac{84}{125}\right)$$ $$e\left(\frac{23}{50}\right)$$ $$e\left(\frac{229}{250}\right)$$ $$e\left(\frac{43}{125}\right)$$ $$e\left(\frac{14}{125}\right)$$ $$e\left(\frac{161}{250}\right)$$ $$e\left(\frac{33}{250}\right)$$ $$e\left(\frac{76}{125}\right)$$ $$e\left(\frac{12}{125}\right)$$ $$e\left(\frac{147}{250}\right)$$
$$\chi_{4016}(41,\cdot)$$ 4016.bq 250 no $$1$$ $$1$$ $$e\left(\frac{189}{250}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{121}{125}\right)$$ $$e\left(\frac{64}{125}\right)$$ $$e\left(\frac{219}{250}\right)$$ $$e\left(\frac{103}{250}\right)$$ $$e\left(\frac{42}{125}\right)$$ $$e\left(\frac{23}{125}\right)$$ $$e\left(\frac{27}{250}\right)$$ $$e\left(\frac{181}{250}\right)$$
$$\chi_{4016}(43,\cdot)$$ 4016.bv 500 yes $$1$$ $$1$$ $$e\left(\frac{29}{500}\right)$$ $$e\left(\frac{69}{100}\right)$$ $$e\left(\frac{3}{125}\right)$$ $$e\left(\frac{29}{250}\right)$$ $$e\left(\frac{109}{500}\right)$$ $$e\left(\frac{283}{500}\right)$$ $$e\left(\frac{187}{250}\right)$$ $$e\left(\frac{14}{125}\right)$$ $$e\left(\frac{147}{500}\right)$$ $$e\left(\frac{41}{500}\right)$$
$$\chi_{4016}(45,\cdot)$$ 4016.bu 500 yes $$1$$ $$1$$ $$e\left(\frac{309}{500}\right)$$ $$e\left(\frac{99}{100}\right)$$ $$e\left(\frac{51}{250}\right)$$ $$e\left(\frac{59}{250}\right)$$ $$e\left(\frac{239}{500}\right)$$ $$e\left(\frac{93}{500}\right)$$ $$e\left(\frac{76}{125}\right)$$ $$e\left(\frac{119}{125}\right)$$ $$e\left(\frac{437}{500}\right)$$ $$e\left(\frac{411}{500}\right)$$
$$\chi_{4016}(47,\cdot)$$ 4016.z 50 no $$1$$ $$1$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{17}{25}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{17}{25}\right)$$ $$e\left(\frac{27}{50}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{9}{25}\right)$$
$$\chi_{4016}(49,\cdot)$$ 4016.bk 125 no $$1$$ $$1$$ $$e\left(\frac{93}{125}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{4}{125}\right)$$ $$e\left(\frac{61}{125}\right)$$ $$e\left(\frac{78}{125}\right)$$ $$e\left(\frac{11}{125}\right)$$ $$e\left(\frac{83}{125}\right)$$ $$e\left(\frac{102}{125}\right)$$ $$e\left(\frac{49}{125}\right)$$ $$e\left(\frac{97}{125}\right)$$
$$\chi_{4016}(51,\cdot)$$ 4016.bj 100 yes $$-1$$ $$1$$ $$e\left(\frac{51}{100}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{25}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{21}{100}\right)$$ $$e\left(\frac{77}{100}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{43}{100}\right)$$ $$e\left(\frac{79}{100}\right)$$
$$\chi_{4016}(53,\cdot)$$ 4016.bs 500 yes $$-1$$ $$1$$ $$e\left(\frac{171}{500}\right)$$ $$e\left(\frac{81}{100}\right)$$ $$e\left(\frac{169}{250}\right)$$ $$e\left(\frac{171}{250}\right)$$ $$e\left(\frac{91}{500}\right)$$ $$e\left(\frac{367}{500}\right)$$ $$e\left(\frac{19}{125}\right)$$ $$e\left(\frac{61}{125}\right)$$ $$e\left(\frac{453}{500}\right)$$ $$e\left(\frac{9}{500}\right)$$
$$\chi_{4016}(55,\cdot)$$ 4016.bo 250 no $$1$$ $$1$$ $$e\left(\frac{103}{125}\right)$$ $$e\left(\frac{41}{50}\right)$$ $$e\left(\frac{193}{250}\right)$$ $$e\left(\frac{81}{125}\right)$$ $$e\left(\frac{201}{250}\right)$$ $$e\left(\frac{187}{250}\right)$$ $$e\left(\frac{161}{250}\right)$$ $$e\left(\frac{117}{125}\right)$$ $$e\left(\frac{83}{250}\right)$$ $$e\left(\frac{149}{250}\right)$$
$$\chi_{4016}(57,\cdot)$$ 4016.br 250 no $$-1$$ $$1$$ $$e\left(\frac{239}{250}\right)$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{71}{125}\right)$$ $$e\left(\frac{114}{125}\right)$$ $$e\left(\frac{72}{125}\right)$$ $$e\left(\frac{203}{250}\right)$$ $$e\left(\frac{67}{125}\right)$$ $$e\left(\frac{123}{125}\right)$$ $$e\left(\frac{26}{125}\right)$$ $$e\left(\frac{131}{250}\right)$$
$$\chi_{4016}(59,\cdot)$$ 4016.bv 500 yes $$1$$ $$1$$ $$e\left(\frac{257}{500}\right)$$ $$e\left(\frac{77}{100}\right)$$ $$e\left(\frac{74}{125}\right)$$ $$e\left(\frac{7}{250}\right)$$ $$e\left(\frac{397}{500}\right)$$ $$e\left(\frac{439}{500}\right)$$ $$e\left(\frac{71}{250}\right)$$ $$e\left(\frac{12}{125}\right)$$ $$e\left(\frac{251}{500}\right)$$ $$e\left(\frac{53}{500}\right)$$
$$\chi_{4016}(61,\cdot)$$ 4016.bs 500 yes $$-1$$ $$1$$ $$e\left(\frac{21}{500}\right)$$ $$e\left(\frac{31}{100}\right)$$ $$e\left(\frac{69}{250}\right)$$ $$e\left(\frac{21}{250}\right)$$ $$e\left(\frac{441}{500}\right)$$ $$e\left(\frac{317}{500}\right)$$ $$e\left(\frac{44}{125}\right)$$ $$e\left(\frac{36}{125}\right)$$ $$e\left(\frac{3}{500}\right)$$ $$e\left(\frac{159}{500}\right)$$
$$\chi_{4016}(63,\cdot)$$ 4016.bb 50 no $$-1$$ $$1$$ $$e\left(\frac{21}{50}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{41}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{17}{25}\right)$$