# Properties

 Modulus 6008 Structure $$C_{750}\times C_{2}\times C_{2}$$ Order 3000

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(6008)

pari: g = idealstar(,6008,2)

## Character group

 sage: G.order()  pari: g.no Order = 3000 sage: H.invariants()  pari: g.cyc Structure = $$C_{750}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6008}(1505,\cdot)$, $\chi_{6008}(1503,\cdot)$, $\chi_{6008}(3005,\cdot)$

## First 32 of 3000 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
$$\chi_{6008}(1,\cdot)$$ 6008.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6008}(3,\cdot)$$ 6008.cj 750 Yes $$1$$ $$1$$ $$e\left(\frac{1}{750}\right)$$ $$e\left(\frac{361}{750}\right)$$ $$e\left(\frac{46}{125}\right)$$ $$e\left(\frac{1}{375}\right)$$ $$e\left(\frac{143}{150}\right)$$ $$e\left(\frac{133}{750}\right)$$ $$e\left(\frac{181}{375}\right)$$ $$e\left(\frac{329}{750}\right)$$ $$e\left(\frac{134}{375}\right)$$ $$e\left(\frac{277}{750}\right)$$
$$\chi_{6008}(5,\cdot)$$ 6008.ch 750 Yes $$1$$ $$1$$ $$e\left(\frac{361}{750}\right)$$ $$e\left(\frac{571}{750}\right)$$ $$e\left(\frac{106}{125}\right)$$ $$e\left(\frac{361}{375}\right)$$ $$e\left(\frac{23}{150}\right)$$ $$e\left(\frac{13}{750}\right)$$ $$e\left(\frac{91}{375}\right)$$ $$e\left(\frac{322}{375}\right)$$ $$e\left(\frac{373}{750}\right)$$ $$e\left(\frac{247}{750}\right)$$
$$\chi_{6008}(7,\cdot)$$ 6008.bz 250 No $$1$$ $$1$$ $$e\left(\frac{46}{125}\right)$$ $$e\left(\frac{106}{125}\right)$$ $$e\left(\frac{71}{125}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{118}{125}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{143}{250}\right)$$ $$e\left(\frac{31}{250}\right)$$ $$e\left(\frac{117}{125}\right)$$
$$\chi_{6008}(9,\cdot)$$ 6008.ce 375 No $$1$$ $$1$$ $$e\left(\frac{1}{375}\right)$$ $$e\left(\frac{361}{375}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{2}{375}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{133}{375}\right)$$ $$e\left(\frac{362}{375}\right)$$ $$e\left(\frac{329}{375}\right)$$ $$e\left(\frac{268}{375}\right)$$ $$e\left(\frac{277}{375}\right)$$
$$\chi_{6008}(11,\cdot)$$ 6008.bt 150 Yes $$1$$ $$1$$ $$e\left(\frac{143}{150}\right)$$ $$e\left(\frac{23}{150}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{119}{150}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{97}{150}\right)$$ $$e\left(\frac{37}{75}\right)$$ $$e\left(\frac{11}{150}\right)$$
$$\chi_{6008}(13,\cdot)$$ 6008.ch 750 Yes $$1$$ $$1$$ $$e\left(\frac{133}{750}\right)$$ $$e\left(\frac{13}{750}\right)$$ $$e\left(\frac{118}{125}\right)$$ $$e\left(\frac{133}{375}\right)$$ $$e\left(\frac{119}{150}\right)$$ $$e\left(\frac{439}{750}\right)$$ $$e\left(\frac{73}{375}\right)$$ $$e\left(\frac{316}{375}\right)$$ $$e\left(\frac{19}{750}\right)$$ $$e\left(\frac{91}{750}\right)$$
$$\chi_{6008}(15,\cdot)$$ 6008.ci 750 No $$1$$ $$1$$ $$e\left(\frac{181}{375}\right)$$ $$e\left(\frac{91}{375}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{362}{375}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{73}{375}\right)$$ $$e\left(\frac{272}{375}\right)$$ $$e\left(\frac{223}{750}\right)$$ $$e\left(\frac{641}{750}\right)$$ $$e\left(\frac{262}{375}\right)$$
$$\chi_{6008}(17,\cdot)$$ 6008.cl 750 No $$-1$$ $$1$$ $$e\left(\frac{329}{750}\right)$$ $$e\left(\frac{322}{375}\right)$$ $$e\left(\frac{143}{250}\right)$$ $$e\left(\frac{329}{375}\right)$$ $$e\left(\frac{97}{150}\right)$$ $$e\left(\frac{316}{375}\right)$$ $$e\left(\frac{223}{750}\right)$$ $$e\left(\frac{241}{750}\right)$$ $$e\left(\frac{211}{375}\right)$$ $$e\left(\frac{4}{375}\right)$$
$$\chi_{6008}(19,\cdot)$$ 6008.cf 750 Yes $$-1$$ $$1$$ $$e\left(\frac{134}{375}\right)$$ $$e\left(\frac{373}{750}\right)$$ $$e\left(\frac{31}{250}\right)$$ $$e\left(\frac{268}{375}\right)$$ $$e\left(\frac{37}{75}\right)$$ $$e\left(\frac{19}{750}\right)$$ $$e\left(\frac{641}{750}\right)$$ $$e\left(\frac{211}{375}\right)$$ $$e\left(\frac{287}{375}\right)$$ $$e\left(\frac{361}{750}\right)$$
$$\chi_{6008}(21,\cdot)$$ 6008.ch 750 Yes $$1$$ $$1$$ $$e\left(\frac{277}{750}\right)$$ $$e\left(\frac{247}{750}\right)$$ $$e\left(\frac{117}{125}\right)$$ $$e\left(\frac{277}{375}\right)$$ $$e\left(\frac{11}{150}\right)$$ $$e\left(\frac{91}{750}\right)$$ $$e\left(\frac{262}{375}\right)$$ $$e\left(\frac{4}{375}\right)$$ $$e\left(\frac{361}{750}\right)$$ $$e\left(\frac{229}{750}\right)$$
$$\chi_{6008}(23,\cdot)$$ 6008.cg 750 No $$-1$$ $$1$$ $$e\left(\frac{157}{750}\right)$$ $$e\left(\frac{26}{375}\right)$$ $$e\left(\frac{69}{250}\right)$$ $$e\left(\frac{157}{375}\right)$$ $$e\left(\frac{101}{150}\right)$$ $$e\left(\frac{128}{375}\right)$$ $$e\left(\frac{209}{750}\right)$$ $$e\left(\frac{139}{375}\right)$$ $$e\left(\frac{451}{750}\right)$$ $$e\left(\frac{182}{375}\right)$$
$$\chi_{6008}(25,\cdot)$$ 6008.ce 375 No $$1$$ $$1$$ $$e\left(\frac{361}{375}\right)$$ $$e\left(\frac{196}{375}\right)$$ $$e\left(\frac{87}{125}\right)$$ $$e\left(\frac{347}{375}\right)$$ $$e\left(\frac{23}{75}\right)$$ $$e\left(\frac{13}{375}\right)$$ $$e\left(\frac{182}{375}\right)$$ $$e\left(\frac{269}{375}\right)$$ $$e\left(\frac{373}{375}\right)$$ $$e\left(\frac{247}{375}\right)$$
$$\chi_{6008}(27,\cdot)$$ 6008.ca 250 Yes $$1$$ $$1$$ $$e\left(\frac{1}{250}\right)$$ $$e\left(\frac{111}{250}\right)$$ $$e\left(\frac{13}{125}\right)$$ $$e\left(\frac{1}{125}\right)$$ $$e\left(\frac{43}{50}\right)$$ $$e\left(\frac{133}{250}\right)$$ $$e\left(\frac{56}{125}\right)$$ $$e\left(\frac{79}{250}\right)$$ $$e\left(\frac{9}{125}\right)$$ $$e\left(\frac{27}{250}\right)$$
$$\chi_{6008}(29,\cdot)$$ 6008.ck 750 Yes $$-1$$ $$1$$ $$e\left(\frac{101}{375}\right)$$ $$e\left(\frac{547}{750}\right)$$ $$e\left(\frac{209}{250}\right)$$ $$e\left(\frac{202}{375}\right)$$ $$e\left(\frac{43}{75}\right)$$ $$e\left(\frac{241}{750}\right)$$ $$e\left(\frac{749}{750}\right)$$ $$e\left(\frac{83}{750}\right)$$ $$e\left(\frac{511}{750}\right)$$ $$e\left(\frac{79}{750}\right)$$
$$\chi_{6008}(31,\cdot)$$ 6008.ci 750 No $$1$$ $$1$$ $$e\left(\frac{76}{375}\right)$$ $$e\left(\frac{61}{375}\right)$$ $$e\left(\frac{117}{125}\right)$$ $$e\left(\frac{152}{375}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{358}{375}\right)$$ $$e\left(\frac{137}{375}\right)$$ $$e\left(\frac{133}{750}\right)$$ $$e\left(\frac{611}{750}\right)$$ $$e\left(\frac{52}{375}\right)$$
$$\chi_{6008}(33,\cdot)$$ 6008.ce 375 No $$1$$ $$1$$ $$e\left(\frac{358}{375}\right)$$ $$e\left(\frac{238}{375}\right)$$ $$e\left(\frac{61}{125}\right)$$ $$e\left(\frac{341}{375}\right)$$ $$e\left(\frac{44}{75}\right)$$ $$e\left(\frac{364}{375}\right)$$ $$e\left(\frac{221}{375}\right)$$ $$e\left(\frac{32}{375}\right)$$ $$e\left(\frac{319}{375}\right)$$ $$e\left(\frac{166}{375}\right)$$
$$\chi_{6008}(35,\cdot)$$ 6008.cj 750 Yes $$1$$ $$1$$ $$e\left(\frac{637}{750}\right)$$ $$e\left(\frac{457}{750}\right)$$ $$e\left(\frac{52}{125}\right)$$ $$e\left(\frac{262}{375}\right)$$ $$e\left(\frac{41}{150}\right)$$ $$e\left(\frac{721}{750}\right)$$ $$e\left(\frac{172}{375}\right)$$ $$e\left(\frac{323}{750}\right)$$ $$e\left(\frac{233}{375}\right)$$ $$e\left(\frac{199}{750}\right)$$
$$\chi_{6008}(37,\cdot)$$ 6008.ch 750 Yes $$1$$ $$1$$ $$e\left(\frac{647}{750}\right)$$ $$e\left(\frac{317}{750}\right)$$ $$e\left(\frac{12}{125}\right)$$ $$e\left(\frac{272}{375}\right)$$ $$e\left(\frac{121}{150}\right)$$ $$e\left(\frac{551}{750}\right)$$ $$e\left(\frac{107}{375}\right)$$ $$e\left(\frac{119}{375}\right)$$ $$e\left(\frac{521}{750}\right)$$ $$e\left(\frac{719}{750}\right)$$
$$\chi_{6008}(39,\cdot)$$ 6008.ci 750 No $$1$$ $$1$$ $$e\left(\frac{67}{375}\right)$$ $$e\left(\frac{187}{375}\right)$$ $$e\left(\frac{39}{125}\right)$$ $$e\left(\frac{134}{375}\right)$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{286}{375}\right)$$ $$e\left(\frac{254}{375}\right)$$ $$e\left(\frac{211}{750}\right)$$ $$e\left(\frac{287}{750}\right)$$ $$e\left(\frac{184}{375}\right)$$
$$\chi_{6008}(41,\cdot)$$ 6008.bm 50 No $$-1$$ $$1$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{6}{25}\right)$$
$$\chi_{6008}(43,\cdot)$$ 6008.cc 250 Yes $$-1$$ $$1$$ $$e\left(\frac{19}{125}\right)$$ $$e\left(\frac{93}{250}\right)$$ $$e\left(\frac{113}{250}\right)$$ $$e\left(\frac{38}{125}\right)$$ $$e\left(\frac{17}{25}\right)$$ $$e\left(\frac{179}{250}\right)$$ $$e\left(\frac{131}{250}\right)$$ $$e\left(\frac{1}{125}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{151}{250}\right)$$
$$\chi_{6008}(45,\cdot)$$ 6008.cb 250 Yes $$1$$ $$1$$ $$e\left(\frac{121}{250}\right)$$ $$e\left(\frac{181}{250}\right)$$ $$e\left(\frac{73}{125}\right)$$ $$e\left(\frac{121}{125}\right)$$ $$e\left(\frac{3}{50}\right)$$ $$e\left(\frac{93}{250}\right)$$ $$e\left(\frac{26}{125}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{53}{250}\right)$$ $$e\left(\frac{17}{250}\right)$$
$$\chi_{6008}(47,\cdot)$$ 6008.cg 750 No $$-1$$ $$1$$ $$e\left(\frac{211}{750}\right)$$ $$e\left(\frac{23}{375}\right)$$ $$e\left(\frac{37}{250}\right)$$ $$e\left(\frac{211}{375}\right)$$ $$e\left(\frac{23}{150}\right)$$ $$e\left(\frac{344}{375}\right)$$ $$e\left(\frac{257}{750}\right)$$ $$e\left(\frac{22}{375}\right)$$ $$e\left(\frac{673}{750}\right)$$ $$e\left(\frac{161}{375}\right)$$
$$\chi_{6008}(49,\cdot)$$ 6008.bp 125 No $$1$$ $$1$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{87}{125}\right)$$ $$e\left(\frac{17}{125}\right)$$ $$e\left(\frac{59}{125}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{111}{125}\right)$$ $$e\left(\frac{54}{125}\right)$$ $$e\left(\frac{18}{125}\right)$$ $$e\left(\frac{31}{125}\right)$$ $$e\left(\frac{109}{125}\right)$$
$$\chi_{6008}(51,\cdot)$$ 6008.bh 50 Yes $$-1$$ $$1$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{17}{50}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{50}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{23}{25}\right)$$ $$e\left(\frac{19}{50}\right)$$
$$\chi_{6008}(53,\cdot)$$ 6008.bl 50 Yes $$1$$ $$1$$ $$e\left(\frac{29}{50}\right)$$ $$e\left(\frac{19}{50}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{50}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{33}{50}\right)$$
$$\chi_{6008}(55,\cdot)$$ 6008.ci 750 No $$1$$ $$1$$ $$e\left(\frac{163}{375}\right)$$ $$e\left(\frac{343}{375}\right)$$ $$e\left(\frac{121}{125}\right)$$ $$e\left(\frac{326}{375}\right)$$ $$e\left(\frac{59}{75}\right)$$ $$e\left(\frac{304}{375}\right)$$ $$e\left(\frac{131}{375}\right)$$ $$e\left(\frac{379}{750}\right)$$ $$e\left(\frac{743}{750}\right)$$ $$e\left(\frac{151}{375}\right)$$
$$\chi_{6008}(57,\cdot)$$ 6008.cl 750 No $$-1$$ $$1$$ $$e\left(\frac{269}{750}\right)$$ $$e\left(\frac{367}{375}\right)$$ $$e\left(\frac{123}{250}\right)$$ $$e\left(\frac{269}{375}\right)$$ $$e\left(\frac{67}{150}\right)$$ $$e\left(\frac{76}{375}\right)$$ $$e\left(\frac{253}{750}\right)$$ $$e\left(\frac{1}{750}\right)$$ $$e\left(\frac{46}{375}\right)$$ $$e\left(\frac{319}{375}\right)$$
$$\chi_{6008}(59,\cdot)$$ 6008.cf 750 Yes $$-1$$ $$1$$ $$e\left(\frac{203}{375}\right)$$ $$e\left(\frac{691}{750}\right)$$ $$e\left(\frac{227}{250}\right)$$ $$e\left(\frac{31}{375}\right)$$ $$e\left(\frac{4}{75}\right)$$ $$e\left(\frac{373}{750}\right)$$ $$e\left(\frac{347}{750}\right)$$ $$e\left(\frac{37}{375}\right)$$ $$e\left(\frac{29}{375}\right)$$ $$e\left(\frac{337}{750}\right)$$
$$\chi_{6008}(61,\cdot)$$ 6008.br 150 Yes $$1$$ $$1$$ $$e\left(\frac{37}{150}\right)$$ $$e\left(\frac{7}{150}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{37}{75}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{121}{150}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{49}{75}\right)$$ $$e\left(\frac{91}{150}\right)$$ $$e\left(\frac{49}{150}\right)$$
$$\chi_{6008}(63,\cdot)$$ 6008.ci 750 No $$1$$ $$1$$ $$e\left(\frac{139}{375}\right)$$ $$e\left(\frac{304}{375}\right)$$ $$e\left(\frac{38}{125}\right)$$ $$e\left(\frac{278}{375}\right)$$ $$e\left(\frac{2}{75}\right)$$ $$e\left(\frac{112}{375}\right)$$ $$e\left(\frac{68}{375}\right)$$ $$e\left(\frac{337}{750}\right)$$ $$e\left(\frac{629}{750}\right)$$ $$e\left(\frac{253}{375}\right)$$