# Properties

 Modulus 3004 Structure $$C_{750}\times C_{2}$$ Order 1500

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(3004)

pari: g = idealstar(,3004,2)

## Character group

 sage: G.order()  pari: g.no Order = 1500 sage: H.invariants()  pari: g.cyc Structure = $$C_{750}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{3004}(1505,\cdot)$, $\chi_{3004}(1503,\cdot)$

## First 32 of 1500 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
$$\chi_{3004}(1,\cdot)$$ 3004.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{3004}(3,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{188}{375}\right)$$ $$e\left(\frac{368}{375}\right)$$ $$e\left(\frac{46}{125}\right)$$ $$e\left(\frac{1}{375}\right)$$ $$e\left(\frac{34}{75}\right)$$ $$e\left(\frac{254}{375}\right)$$ $$e\left(\frac{181}{375}\right)$$ $$e\left(\frac{329}{750}\right)$$ $$e\left(\frac{643}{750}\right)$$ $$e\left(\frac{326}{375}\right)$$
$$\chi_{3004}(5,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{368}{375}\right)$$ $$e\left(\frac{98}{375}\right)$$ $$e\left(\frac{106}{125}\right)$$ $$e\left(\frac{361}{375}\right)$$ $$e\left(\frac{49}{75}\right)$$ $$e\left(\frac{194}{375}\right)$$ $$e\left(\frac{91}{375}\right)$$ $$e\left(\frac{322}{375}\right)$$ $$e\left(\frac{374}{375}\right)$$ $$e\left(\frac{311}{375}\right)$$
$$\chi_{3004}(7,\cdot)$$ 3004.ba 250 yes $$1$$ $$1$$ $$e\left(\frac{46}{125}\right)$$ $$e\left(\frac{106}{125}\right)$$ $$e\left(\frac{71}{125}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{118}{125}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{143}{250}\right)$$ $$e\left(\frac{31}{250}\right)$$ $$e\left(\frac{117}{125}\right)$$
$$\chi_{3004}(9,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{1}{375}\right)$$ $$e\left(\frac{361}{375}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{2}{375}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{133}{375}\right)$$ $$e\left(\frac{362}{375}\right)$$ $$e\left(\frac{329}{375}\right)$$ $$e\left(\frac{268}{375}\right)$$ $$e\left(\frac{277}{375}\right)$$
$$\chi_{3004}(11,\cdot)$$ 3004.y 150 yes $$1$$ $$1$$ $$e\left(\frac{34}{75}\right)$$ $$e\left(\frac{49}{75}\right)$$ $$e\left(\frac{3}{25}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{97}{150}\right)$$ $$e\left(\frac{149}{150}\right)$$ $$e\left(\frac{43}{75}\right)$$
$$\chi_{3004}(13,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{254}{375}\right)$$ $$e\left(\frac{194}{375}\right)$$ $$e\left(\frac{118}{125}\right)$$ $$e\left(\frac{133}{375}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{32}{375}\right)$$ $$e\left(\frac{73}{375}\right)$$ $$e\left(\frac{316}{375}\right)$$ $$e\left(\frac{197}{375}\right)$$ $$e\left(\frac{233}{375}\right)$$
$$\chi_{3004}(15,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{181}{375}\right)$$ $$e\left(\frac{91}{375}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{362}{375}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{73}{375}\right)$$ $$e\left(\frac{272}{375}\right)$$ $$e\left(\frac{223}{750}\right)$$ $$e\left(\frac{641}{750}\right)$$ $$e\left(\frac{262}{375}\right)$$
$$\chi_{3004}(17,\cdot)$$ 3004.bf 750 no $$-1$$ $$1$$ $$e\left(\frac{329}{750}\right)$$ $$e\left(\frac{322}{375}\right)$$ $$e\left(\frac{143}{250}\right)$$ $$e\left(\frac{329}{375}\right)$$ $$e\left(\frac{97}{150}\right)$$ $$e\left(\frac{316}{375}\right)$$ $$e\left(\frac{223}{750}\right)$$ $$e\left(\frac{241}{750}\right)$$ $$e\left(\frac{211}{375}\right)$$ $$e\left(\frac{4}{375}\right)$$
$$\chi_{3004}(19,\cdot)$$ 3004.bd 750 yes $$-1$$ $$1$$ $$e\left(\frac{643}{750}\right)$$ $$e\left(\frac{374}{375}\right)$$ $$e\left(\frac{31}{250}\right)$$ $$e\left(\frac{268}{375}\right)$$ $$e\left(\frac{149}{150}\right)$$ $$e\left(\frac{197}{375}\right)$$ $$e\left(\frac{641}{750}\right)$$ $$e\left(\frac{211}{375}\right)$$ $$e\left(\frac{199}{750}\right)$$ $$e\left(\frac{368}{375}\right)$$
$$\chi_{3004}(21,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{326}{375}\right)$$ $$e\left(\frac{311}{375}\right)$$ $$e\left(\frac{117}{125}\right)$$ $$e\left(\frac{277}{375}\right)$$ $$e\left(\frac{43}{75}\right)$$ $$e\left(\frac{233}{375}\right)$$ $$e\left(\frac{262}{375}\right)$$ $$e\left(\frac{4}{375}\right)$$ $$e\left(\frac{368}{375}\right)$$ $$e\left(\frac{302}{375}\right)$$
$$\chi_{3004}(23,\cdot)$$ 3004.bd 750 yes $$-1$$ $$1$$ $$e\left(\frac{157}{750}\right)$$ $$e\left(\frac{26}{375}\right)$$ $$e\left(\frac{69}{250}\right)$$ $$e\left(\frac{157}{375}\right)$$ $$e\left(\frac{101}{150}\right)$$ $$e\left(\frac{128}{375}\right)$$ $$e\left(\frac{209}{750}\right)$$ $$e\left(\frac{139}{375}\right)$$ $$e\left(\frac{451}{750}\right)$$ $$e\left(\frac{182}{375}\right)$$
$$\chi_{3004}(25,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{361}{375}\right)$$ $$e\left(\frac{196}{375}\right)$$ $$e\left(\frac{87}{125}\right)$$ $$e\left(\frac{347}{375}\right)$$ $$e\left(\frac{23}{75}\right)$$ $$e\left(\frac{13}{375}\right)$$ $$e\left(\frac{182}{375}\right)$$ $$e\left(\frac{269}{375}\right)$$ $$e\left(\frac{373}{375}\right)$$ $$e\left(\frac{247}{375}\right)$$
$$\chi_{3004}(27,\cdot)$$ 3004.ba 250 yes $$1$$ $$1$$ $$e\left(\frac{63}{125}\right)$$ $$e\left(\frac{118}{125}\right)$$ $$e\left(\frac{13}{125}\right)$$ $$e\left(\frac{1}{125}\right)$$ $$e\left(\frac{9}{25}\right)$$ $$e\left(\frac{4}{125}\right)$$ $$e\left(\frac{56}{125}\right)$$ $$e\left(\frac{79}{250}\right)$$ $$e\left(\frac{143}{250}\right)$$ $$e\left(\frac{76}{125}\right)$$
$$\chi_{3004}(29,\cdot)$$ 3004.bf 750 no $$-1$$ $$1$$ $$e\left(\frac{577}{750}\right)$$ $$e\left(\frac{86}{375}\right)$$ $$e\left(\frac{209}{250}\right)$$ $$e\left(\frac{202}{375}\right)$$ $$e\left(\frac{11}{150}\right)$$ $$e\left(\frac{308}{375}\right)$$ $$e\left(\frac{749}{750}\right)$$ $$e\left(\frac{83}{750}\right)$$ $$e\left(\frac{68}{375}\right)$$ $$e\left(\frac{227}{375}\right)$$
$$\chi_{3004}(31,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{76}{375}\right)$$ $$e\left(\frac{61}{375}\right)$$ $$e\left(\frac{117}{125}\right)$$ $$e\left(\frac{152}{375}\right)$$ $$e\left(\frac{68}{75}\right)$$ $$e\left(\frac{358}{375}\right)$$ $$e\left(\frac{137}{375}\right)$$ $$e\left(\frac{133}{750}\right)$$ $$e\left(\frac{611}{750}\right)$$ $$e\left(\frac{52}{375}\right)$$
$$\chi_{3004}(33,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{358}{375}\right)$$ $$e\left(\frac{238}{375}\right)$$ $$e\left(\frac{61}{125}\right)$$ $$e\left(\frac{341}{375}\right)$$ $$e\left(\frac{44}{75}\right)$$ $$e\left(\frac{364}{375}\right)$$ $$e\left(\frac{221}{375}\right)$$ $$e\left(\frac{32}{375}\right)$$ $$e\left(\frac{319}{375}\right)$$ $$e\left(\frac{166}{375}\right)$$
$$\chi_{3004}(35,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{131}{375}\right)$$ $$e\left(\frac{41}{375}\right)$$ $$e\left(\frac{52}{125}\right)$$ $$e\left(\frac{262}{375}\right)$$ $$e\left(\frac{58}{75}\right)$$ $$e\left(\frac{173}{375}\right)$$ $$e\left(\frac{172}{375}\right)$$ $$e\left(\frac{323}{750}\right)$$ $$e\left(\frac{91}{750}\right)$$ $$e\left(\frac{287}{375}\right)$$
$$\chi_{3004}(37,\cdot)$$ 3004.bc 375 no $$1$$ $$1$$ $$e\left(\frac{136}{375}\right)$$ $$e\left(\frac{346}{375}\right)$$ $$e\left(\frac{12}{125}\right)$$ $$e\left(\frac{272}{375}\right)$$ $$e\left(\frac{23}{75}\right)$$ $$e\left(\frac{88}{375}\right)$$ $$e\left(\frac{107}{375}\right)$$ $$e\left(\frac{119}{375}\right)$$ $$e\left(\frac{73}{375}\right)$$ $$e\left(\frac{172}{375}\right)$$
$$\chi_{3004}(39,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{67}{375}\right)$$ $$e\left(\frac{187}{375}\right)$$ $$e\left(\frac{39}{125}\right)$$ $$e\left(\frac{134}{375}\right)$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{286}{375}\right)$$ $$e\left(\frac{254}{375}\right)$$ $$e\left(\frac{211}{750}\right)$$ $$e\left(\frac{287}{750}\right)$$ $$e\left(\frac{184}{375}\right)$$
$$\chi_{3004}(41,\cdot)$$ 3004.t 50 no $$-1$$ $$1$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{31}{50}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{49}{50}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{6}{25}\right)$$
$$\chi_{3004}(43,\cdot)$$ 3004.bb 250 yes $$-1$$ $$1$$ $$e\left(\frac{163}{250}\right)$$ $$e\left(\frac{109}{125}\right)$$ $$e\left(\frac{113}{250}\right)$$ $$e\left(\frac{38}{125}\right)$$ $$e\left(\frac{9}{50}\right)$$ $$e\left(\frac{27}{125}\right)$$ $$e\left(\frac{131}{250}\right)$$ $$e\left(\frac{1}{125}\right)$$ $$e\left(\frac{59}{250}\right)$$ $$e\left(\frac{13}{125}\right)$$
$$\chi_{3004}(45,\cdot)$$ 3004.v 125 no $$1$$ $$1$$ $$e\left(\frac{123}{125}\right)$$ $$e\left(\frac{28}{125}\right)$$ $$e\left(\frac{73}{125}\right)$$ $$e\left(\frac{121}{125}\right)$$ $$e\left(\frac{14}{25}\right)$$ $$e\left(\frac{109}{125}\right)$$ $$e\left(\frac{26}{125}\right)$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{89}{125}\right)$$ $$e\left(\frac{71}{125}\right)$$
$$\chi_{3004}(47,\cdot)$$ 3004.bd 750 yes $$-1$$ $$1$$ $$e\left(\frac{211}{750}\right)$$ $$e\left(\frac{23}{375}\right)$$ $$e\left(\frac{37}{250}\right)$$ $$e\left(\frac{211}{375}\right)$$ $$e\left(\frac{23}{150}\right)$$ $$e\left(\frac{344}{375}\right)$$ $$e\left(\frac{257}{750}\right)$$ $$e\left(\frac{22}{375}\right)$$ $$e\left(\frac{673}{750}\right)$$ $$e\left(\frac{161}{375}\right)$$
$$\chi_{3004}(49,\cdot)$$ 3004.v 125 no $$1$$ $$1$$ $$e\left(\frac{92}{125}\right)$$ $$e\left(\frac{87}{125}\right)$$ $$e\left(\frac{17}{125}\right)$$ $$e\left(\frac{59}{125}\right)$$ $$e\left(\frac{6}{25}\right)$$ $$e\left(\frac{111}{125}\right)$$ $$e\left(\frac{54}{125}\right)$$ $$e\left(\frac{18}{125}\right)$$ $$e\left(\frac{31}{125}\right)$$ $$e\left(\frac{109}{125}\right)$$
$$\chi_{3004}(51,\cdot)$$ 3004.s 50 yes $$-1$$ $$1$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{21}{25}\right)$$ $$e\left(\frac{47}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{13}{25}\right)$$ $$e\left(\frac{39}{50}\right)$$ $$e\left(\frac{19}{25}\right)$$ $$e\left(\frac{21}{50}\right)$$ $$e\left(\frac{22}{25}\right)$$
$$\chi_{3004}(53,\cdot)$$ 3004.n 25 no $$1$$ $$1$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{22}{25}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{16}{25}\right)$$ $$e\left(\frac{24}{25}\right)$$ $$e\left(\frac{8}{25}\right)$$ $$e\left(\frac{11}{25}\right)$$ $$e\left(\frac{4}{25}\right)$$
$$\chi_{3004}(55,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{163}{375}\right)$$ $$e\left(\frac{343}{375}\right)$$ $$e\left(\frac{121}{125}\right)$$ $$e\left(\frac{326}{375}\right)$$ $$e\left(\frac{59}{75}\right)$$ $$e\left(\frac{304}{375}\right)$$ $$e\left(\frac{131}{375}\right)$$ $$e\left(\frac{379}{750}\right)$$ $$e\left(\frac{743}{750}\right)$$ $$e\left(\frac{151}{375}\right)$$
$$\chi_{3004}(57,\cdot)$$ 3004.bf 750 no $$-1$$ $$1$$ $$e\left(\frac{269}{750}\right)$$ $$e\left(\frac{367}{375}\right)$$ $$e\left(\frac{123}{250}\right)$$ $$e\left(\frac{269}{375}\right)$$ $$e\left(\frac{67}{150}\right)$$ $$e\left(\frac{76}{375}\right)$$ $$e\left(\frac{253}{750}\right)$$ $$e\left(\frac{1}{750}\right)$$ $$e\left(\frac{46}{375}\right)$$ $$e\left(\frac{319}{375}\right)$$
$$\chi_{3004}(59,\cdot)$$ 3004.bd 750 yes $$-1$$ $$1$$ $$e\left(\frac{31}{750}\right)$$ $$e\left(\frac{158}{375}\right)$$ $$e\left(\frac{227}{250}\right)$$ $$e\left(\frac{31}{375}\right)$$ $$e\left(\frac{83}{150}\right)$$ $$e\left(\frac{374}{375}\right)$$ $$e\left(\frac{347}{750}\right)$$ $$e\left(\frac{37}{375}\right)$$ $$e\left(\frac{433}{750}\right)$$ $$e\left(\frac{356}{375}\right)$$
$$\chi_{3004}(61,\cdot)$$ 3004.u 75 no $$1$$ $$1$$ $$e\left(\frac{56}{75}\right)$$ $$e\left(\frac{41}{75}\right)$$ $$e\left(\frac{2}{25}\right)$$ $$e\left(\frac{37}{75}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{23}{75}\right)$$ $$e\left(\frac{22}{75}\right)$$ $$e\left(\frac{49}{75}\right)$$ $$e\left(\frac{8}{75}\right)$$ $$e\left(\frac{62}{75}\right)$$
$$\chi_{3004}(63,\cdot)$$ 3004.be 750 yes $$1$$ $$1$$ $$e\left(\frac{139}{375}\right)$$ $$e\left(\frac{304}{375}\right)$$ $$e\left(\frac{38}{125}\right)$$ $$e\left(\frac{278}{375}\right)$$ $$e\left(\frac{2}{75}\right)$$ $$e\left(\frac{112}{375}\right)$$ $$e\left(\frac{68}{375}\right)$$ $$e\left(\frac{337}{750}\right)$$ $$e\left(\frac{629}{750}\right)$$ $$e\left(\frac{253}{375}\right)$$