# Properties

 Modulus 4006 Structure $$C_{2002}$$ Order 2002

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(4006)

pari: g = idealstar(,4006,2)

## Character group

 sage: G.order()  pari: g.no Order = 2002 sage: H.invariants()  pari: g.cyc Structure = $$C_{2002}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4006}(5,\cdot)$

## First 32 of 2002 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
$$\chi_{4006}(1,\cdot)$$ 4006.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4006}(3,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{799}{1001}\right)$$ $$e\left(\frac{173}{1001}\right)$$ $$e\left(\frac{258}{1001}\right)$$ $$e\left(\frac{597}{1001}\right)$$ $$e\left(\frac{67}{143}\right)$$ $$e\left(\frac{204}{1001}\right)$$ $$e\left(\frac{972}{1001}\right)$$ $$e\left(\frac{48}{91}\right)$$ $$e\left(\frac{982}{1001}\right)$$ $$e\left(\frac{8}{143}\right)$$
$$\chi_{4006}(5,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{173}{1001}\right)$$ $$e\left(\frac{1}{2002}\right)$$ $$e\left(\frac{123}{2002}\right)$$ $$e\left(\frac{346}{1001}\right)$$ $$e\left(\frac{7}{286}\right)$$ $$e\left(\frac{747}{1001}\right)$$ $$e\left(\frac{347}{2002}\right)$$ $$e\left(\frac{25}{182}\right)$$ $$e\left(\frac{269}{1001}\right)$$ $$e\left(\frac{67}{286}\right)$$
$$\chi_{4006}(7,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{258}{1001}\right)$$ $$e\left(\frac{123}{2002}\right)$$ $$e\left(\frac{1115}{2002}\right)$$ $$e\left(\frac{516}{1001}\right)$$ $$e\left(\frac{3}{286}\right)$$ $$e\left(\frac{790}{1001}\right)$$ $$e\left(\frac{639}{2002}\right)$$ $$e\left(\frac{163}{182}\right)$$ $$e\left(\frac{54}{1001}\right)$$ $$e\left(\frac{233}{286}\right)$$
$$\chi_{4006}(9,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{597}{1001}\right)$$ $$e\left(\frac{346}{1001}\right)$$ $$e\left(\frac{516}{1001}\right)$$ $$e\left(\frac{193}{1001}\right)$$ $$e\left(\frac{134}{143}\right)$$ $$e\left(\frac{408}{1001}\right)$$ $$e\left(\frac{943}{1001}\right)$$ $$e\left(\frac{5}{91}\right)$$ $$e\left(\frac{963}{1001}\right)$$ $$e\left(\frac{16}{143}\right)$$
$$\chi_{4006}(11,\cdot)$$ 4006.n 286 no $$-1$$ $$1$$ $$e\left(\frac{67}{143}\right)$$ $$e\left(\frac{7}{286}\right)$$ $$e\left(\frac{3}{286}\right)$$ $$e\left(\frac{134}{143}\right)$$ $$e\left(\frac{57}{286}\right)$$ $$e\left(\frac{81}{143}\right)$$ $$e\left(\frac{141}{286}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{24}{143}\right)$$ $$e\left(\frac{137}{286}\right)$$
$$\chi_{4006}(13,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{204}{1001}\right)$$ $$e\left(\frac{747}{1001}\right)$$ $$e\left(\frac{790}{1001}\right)$$ $$e\left(\frac{408}{1001}\right)$$ $$e\left(\frac{81}{143}\right)$$ $$e\left(\frac{904}{1001}\right)$$ $$e\left(\frac{951}{1001}\right)$$ $$e\left(\frac{20}{91}\right)$$ $$e\left(\frac{485}{1001}\right)$$ $$e\left(\frac{142}{143}\right)$$
$$\chi_{4006}(15,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{972}{1001}\right)$$ $$e\left(\frac{347}{2002}\right)$$ $$e\left(\frac{639}{2002}\right)$$ $$e\left(\frac{943}{1001}\right)$$ $$e\left(\frac{141}{286}\right)$$ $$e\left(\frac{951}{1001}\right)$$ $$e\left(\frac{289}{2002}\right)$$ $$e\left(\frac{121}{182}\right)$$ $$e\left(\frac{250}{1001}\right)$$ $$e\left(\frac{83}{286}\right)$$
$$\chi_{4006}(17,\cdot)$$ 4006.m 182 no $$-1$$ $$1$$ $$e\left(\frac{48}{91}\right)$$ $$e\left(\frac{25}{182}\right)$$ $$e\left(\frac{163}{182}\right)$$ $$e\left(\frac{5}{91}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{20}{91}\right)$$ $$e\left(\frac{121}{182}\right)$$ $$e\left(\frac{141}{182}\right)$$ $$e\left(\frac{82}{91}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{4006}(19,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{982}{1001}\right)$$ $$e\left(\frac{269}{1001}\right)$$ $$e\left(\frac{54}{1001}\right)$$ $$e\left(\frac{963}{1001}\right)$$ $$e\left(\frac{24}{143}\right)$$ $$e\left(\frac{485}{1001}\right)$$ $$e\left(\frac{250}{1001}\right)$$ $$e\left(\frac{82}{91}\right)$$ $$e\left(\frac{578}{1001}\right)$$ $$e\left(\frac{5}{143}\right)$$
$$\chi_{4006}(21,\cdot)$$ 4006.n 286 no $$-1$$ $$1$$ $$e\left(\frac{8}{143}\right)$$ $$e\left(\frac{67}{286}\right)$$ $$e\left(\frac{233}{286}\right)$$ $$e\left(\frac{16}{143}\right)$$ $$e\left(\frac{137}{286}\right)$$ $$e\left(\frac{142}{143}\right)$$ $$e\left(\frac{83}{286}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{5}{143}\right)$$ $$e\left(\frac{249}{286}\right)$$
$$\chi_{4006}(23,\cdot)$$ 4006.n 286 no $$-1$$ $$1$$ $$e\left(\frac{54}{143}\right)$$ $$e\left(\frac{59}{286}\right)$$ $$e\left(\frac{107}{286}\right)$$ $$e\left(\frac{108}{143}\right)$$ $$e\left(\frac{31}{286}\right)$$ $$e\left(\frac{29}{143}\right)$$ $$e\left(\frac{167}{286}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{141}{143}\right)$$ $$e\left(\frac{215}{286}\right)$$
$$\chi_{4006}(25,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{346}{1001}\right)$$ $$e\left(\frac{1}{1001}\right)$$ $$e\left(\frac{123}{1001}\right)$$ $$e\left(\frac{692}{1001}\right)$$ $$e\left(\frac{7}{143}\right)$$ $$e\left(\frac{493}{1001}\right)$$ $$e\left(\frac{347}{1001}\right)$$ $$e\left(\frac{25}{91}\right)$$ $$e\left(\frac{538}{1001}\right)$$ $$e\left(\frac{67}{143}\right)$$
$$\chi_{4006}(27,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{395}{1001}\right)$$ $$e\left(\frac{519}{1001}\right)$$ $$e\left(\frac{774}{1001}\right)$$ $$e\left(\frac{790}{1001}\right)$$ $$e\left(\frac{58}{143}\right)$$ $$e\left(\frac{612}{1001}\right)$$ $$e\left(\frac{914}{1001}\right)$$ $$e\left(\frac{53}{91}\right)$$ $$e\left(\frac{944}{1001}\right)$$ $$e\left(\frac{24}{143}\right)$$
$$\chi_{4006}(29,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{895}{1001}\right)$$ $$e\left(\frac{1579}{2002}\right)$$ $$e\left(\frac{23}{2002}\right)$$ $$e\left(\frac{789}{1001}\right)$$ $$e\left(\frac{185}{286}\right)$$ $$e\left(\frac{335}{1001}\right)$$ $$e\left(\frac{1367}{2002}\right)$$ $$e\left(\frac{163}{182}\right)$$ $$e\left(\frac{327}{1001}\right)$$ $$e\left(\frac{259}{286}\right)$$
$$\chi_{4006}(31,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{562}{1001}\right)$$ $$e\left(\frac{1525}{2002}\right)$$ $$e\left(\frac{1389}{2002}\right)$$ $$e\left(\frac{123}{1001}\right)$$ $$e\left(\frac{93}{286}\right)$$ $$e\left(\frac{37}{1001}\right)$$ $$e\left(\frac{647}{2002}\right)$$ $$e\left(\frac{87}{182}\right)$$ $$e\left(\frac{816}{1001}\right)$$ $$e\left(\frac{73}{286}\right)$$
$$\chi_{4006}(33,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{267}{1001}\right)$$ $$e\left(\frac{395}{2002}\right)$$ $$e\left(\frac{537}{2002}\right)$$ $$e\left(\frac{534}{1001}\right)$$ $$e\left(\frac{191}{286}\right)$$ $$e\left(\frac{771}{1001}\right)$$ $$e\left(\frac{929}{2002}\right)$$ $$e\left(\frac{47}{182}\right)$$ $$e\left(\frac{149}{1001}\right)$$ $$e\left(\frac{153}{286}\right)$$
$$\chi_{4006}(35,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{431}{1001}\right)$$ $$e\left(\frac{62}{1001}\right)$$ $$e\left(\frac{619}{1001}\right)$$ $$e\left(\frac{862}{1001}\right)$$ $$e\left(\frac{5}{143}\right)$$ $$e\left(\frac{536}{1001}\right)$$ $$e\left(\frac{493}{1001}\right)$$ $$e\left(\frac{3}{91}\right)$$ $$e\left(\frac{323}{1001}\right)$$ $$e\left(\frac{7}{143}\right)$$
$$\chi_{4006}(37,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{709}{1001}\right)$$ $$e\left(\frac{629}{2002}\right)$$ $$e\left(\frac{1291}{2002}\right)$$ $$e\left(\frac{417}{1001}\right)$$ $$e\left(\frac{113}{286}\right)$$ $$e\left(\frac{394}{1001}\right)$$ $$e\left(\frac{45}{2002}\right)$$ $$e\left(\frac{73}{182}\right)$$ $$e\left(\frac{32}{1001}\right)$$ $$e\left(\frac{101}{286}\right)$$
$$\chi_{4006}(39,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{2}{1001}\right)$$ $$e\left(\frac{920}{1001}\right)$$ $$e\left(\frac{47}{1001}\right)$$ $$e\left(\frac{4}{1001}\right)$$ $$e\left(\frac{5}{143}\right)$$ $$e\left(\frac{107}{1001}\right)$$ $$e\left(\frac{922}{1001}\right)$$ $$e\left(\frac{68}{91}\right)$$ $$e\left(\frac{466}{1001}\right)$$ $$e\left(\frac{7}{143}\right)$$
$$\chi_{4006}(41,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{353}{1001}\right)$$ $$e\left(\frac{1437}{2002}\right)$$ $$e\left(\frac{575}{2002}\right)$$ $$e\left(\frac{706}{1001}\right)$$ $$e\left(\frac{49}{286}\right)$$ $$e\left(\frac{367}{1001}\right)$$ $$e\left(\frac{141}{2002}\right)$$ $$e\left(\frac{71}{182}\right)$$ $$e\left(\frac{167}{1001}\right)$$ $$e\left(\frac{183}{286}\right)$$
$$\chi_{4006}(43,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{899}{1001}\right)$$ $$e\left(\frac{1255}{2002}\right)$$ $$e\left(\frac{211}{2002}\right)$$ $$e\left(\frac{797}{1001}\right)$$ $$e\left(\frac{205}{286}\right)$$ $$e\left(\frac{549}{1001}\right)$$ $$e\left(\frac{1051}{2002}\right)$$ $$e\left(\frac{71}{182}\right)$$ $$e\left(\frac{258}{1001}\right)$$ $$e\left(\frac{1}{286}\right)$$
$$\chi_{4006}(45,\cdot)$$ 4006.h 26 no $$-1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$
$$\chi_{4006}(47,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{769}{1001}\right)$$ $$e\left(\frac{387}{1001}\right)$$ $$e\left(\frac{554}{1001}\right)$$ $$e\left(\frac{537}{1001}\right)$$ $$e\left(\frac{135}{143}\right)$$ $$e\left(\frac{601}{1001}\right)$$ $$e\left(\frac{155}{1001}\right)$$ $$e\left(\frac{29}{91}\right)$$ $$e\left(\frac{999}{1001}\right)$$ $$e\left(\frac{46}{143}\right)$$
$$\chi_{4006}(49,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{516}{1001}\right)$$ $$e\left(\frac{123}{1001}\right)$$ $$e\left(\frac{114}{1001}\right)$$ $$e\left(\frac{31}{1001}\right)$$ $$e\left(\frac{3}{143}\right)$$ $$e\left(\frac{579}{1001}\right)$$ $$e\left(\frac{639}{1001}\right)$$ $$e\left(\frac{72}{91}\right)$$ $$e\left(\frac{108}{1001}\right)$$ $$e\left(\frac{90}{143}\right)$$
$$\chi_{4006}(51,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{326}{1001}\right)$$ $$e\left(\frac{621}{2002}\right)$$ $$e\left(\frac{307}{2002}\right)$$ $$e\left(\frac{652}{1001}\right)$$ $$e\left(\frac{57}{286}\right)$$ $$e\left(\frac{424}{1001}\right)$$ $$e\left(\frac{1273}{2002}\right)$$ $$e\left(\frac{55}{182}\right)$$ $$e\left(\frac{883}{1001}\right)$$ $$e\left(\frac{137}{286}\right)$$
$$\chi_{4006}(53,\cdot)$$ 4006.j 91 no $$1$$ $$1$$ $$e\left(\frac{38}{91}\right)$$ $$e\left(\frac{8}{91}\right)$$ $$e\left(\frac{74}{91}\right)$$ $$e\left(\frac{76}{91}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{31}{91}\right)$$ $$e\left(\frac{46}{91}\right)$$ $$e\left(\frac{16}{91}\right)$$ $$e\left(\frac{27}{91}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{4006}(55,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{642}{1001}\right)$$ $$e\left(\frac{25}{1001}\right)$$ $$e\left(\frac{72}{1001}\right)$$ $$e\left(\frac{283}{1001}\right)$$ $$e\left(\frac{32}{143}\right)$$ $$e\left(\frac{313}{1001}\right)$$ $$e\left(\frac{667}{1001}\right)$$ $$e\left(\frac{79}{91}\right)$$ $$e\left(\frac{437}{1001}\right)$$ $$e\left(\frac{102}{143}\right)$$
$$\chi_{4006}(57,\cdot)$$ 4006.i 77 no $$1$$ $$1$$ $$e\left(\frac{60}{77}\right)$$ $$e\left(\frac{34}{77}\right)$$ $$e\left(\frac{24}{77}\right)$$ $$e\left(\frac{43}{77}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{53}{77}\right)$$ $$e\left(\frac{17}{77}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{43}{77}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{4006}(59,\cdot)$$ 4006.o 1001 no $$1$$ $$1$$ $$e\left(\frac{201}{1001}\right)$$ $$e\left(\frac{368}{1001}\right)$$ $$e\left(\frac{219}{1001}\right)$$ $$e\left(\frac{402}{1001}\right)$$ $$e\left(\frac{2}{143}\right)$$ $$e\left(\frac{243}{1001}\right)$$ $$e\left(\frac{569}{1001}\right)$$ $$e\left(\frac{9}{91}\right)$$ $$e\left(\frac{787}{1001}\right)$$ $$e\left(\frac{60}{143}\right)$$
$$\chi_{4006}(61,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{977}{1001}\right)$$ $$e\left(\frac{943}{2002}\right)$$ $$e\left(\frac{1875}{2002}\right)$$ $$e\left(\frac{953}{1001}\right)$$ $$e\left(\frac{23}{286}\right)$$ $$e\left(\frac{718}{1001}\right)$$ $$e\left(\frac{895}{2002}\right)$$ $$e\left(\frac{97}{182}\right)$$ $$e\left(\frac{414}{1001}\right)$$ $$e\left(\frac{261}{286}\right)$$
$$\chi_{4006}(63,\cdot)$$ 4006.p 2002 no $$-1$$ $$1$$ $$e\left(\frac{855}{1001}\right)$$ $$e\left(\frac{815}{2002}\right)$$ $$e\left(\frac{145}{2002}\right)$$ $$e\left(\frac{709}{1001}\right)$$ $$e\left(\frac{271}{286}\right)$$ $$e\left(\frac{197}{1001}\right)$$ $$e\left(\frac{523}{2002}\right)$$ $$e\left(\frac{173}{182}\right)$$ $$e\left(\frac{16}{1001}\right)$$ $$e\left(\frac{265}{286}\right)$$