# Properties

 Modulus 4008 Structure $$C_{166}\times C_{2}\times C_{2}\times C_{2}$$ Order 1328

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(4008)

pari: g = idealstar(,4008,2)

## Character group

 sage: G.order()  pari: g.no Order = 1328 sage: H.invariants()  pari: g.cyc Structure = $$C_{166}\times C_{2}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{4008}(673,\cdot)$, $\chi_{4008}(1337,\cdot)$, $\chi_{4008}(3007,\cdot)$, $\chi_{4008}(2005,\cdot)$

## First 32 of 1328 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 5 7 11 13 17 19 23 25 29 31
$$\chi_{4008}(1,\cdot)$$ 4008.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{4008}(5,\cdot)$$ 4008.y 166 yes $$1$$ $$1$$ $$e\left(\frac{1}{166}\right)$$ $$e\left(\frac{59}{83}\right)$$ $$e\left(\frac{14}{83}\right)$$ $$e\left(\frac{10}{83}\right)$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{141}{166}\right)$$ $$e\left(\frac{8}{83}\right)$$ $$e\left(\frac{1}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{45}{83}\right)$$
$$\chi_{4008}(7,\cdot)$$ 4008.w 166 no $$-1$$ $$1$$ $$e\left(\frac{59}{83}\right)$$ $$e\left(\frac{63}{166}\right)$$ $$e\left(\frac{67}{166}\right)$$ $$e\left(\frac{18}{83}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{121}{166}\right)$$ $$e\left(\frac{145}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{52}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$
$$\chi_{4008}(11,\cdot)$$ 4008.x 166 yes $$1$$ $$1$$ $$e\left(\frac{14}{83}\right)$$ $$e\left(\frac{67}{166}\right)$$ $$e\left(\frac{37}{166}\right)$$ $$e\left(\frac{145}{166}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{113}{166}\right)$$
$$\chi_{4008}(13,\cdot)$$ 4008.s 166 no $$-1$$ $$1$$ $$e\left(\frac{10}{83}\right)$$ $$e\left(\frac{18}{83}\right)$$ $$e\left(\frac{145}{166}\right)$$ $$e\left(\frac{34}{83}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{81}{166}\right)$$ $$e\left(\frac{71}{166}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{95}{166}\right)$$ $$e\left(\frac{70}{83}\right)$$
$$\chi_{4008}(17,\cdot)$$ 4008.t 166 no $$1$$ $$1$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{61}{83}\right)$$
$$\chi_{4008}(19,\cdot)$$ 4008.bd 166 no $$-1$$ $$1$$ $$e\left(\frac{141}{166}\right)$$ $$e\left(\frac{121}{166}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{81}{166}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{151}{166}\right)$$ $$e\left(\frac{157}{166}\right)$$
$$\chi_{4008}(23,\cdot)$$ 4008.v 166 no $$-1$$ $$1$$ $$e\left(\frac{8}{83}\right)$$ $$e\left(\frac{145}{166}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{71}{166}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{7}{166}\right)$$ $$e\left(\frac{16}{83}\right)$$ $$e\left(\frac{159}{166}\right)$$ $$e\left(\frac{29}{166}\right)$$
$$\chi_{4008}(25,\cdot)$$ 4008.q 83 no $$1$$ $$1$$ $$e\left(\frac{1}{83}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{16}{83}\right)$$ $$e\left(\frac{2}{83}\right)$$ $$e\left(\frac{67}{83}\right)$$ $$e\left(\frac{7}{83}\right)$$
$$\chi_{4008}(29,\cdot)$$ 4008.r 166 yes $$-1$$ $$1$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{52}{83}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{95}{166}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{151}{166}\right)$$ $$e\left(\frac{159}{166}\right)$$ $$e\left(\frac{67}{83}\right)$$ $$e\left(\frac{45}{83}\right)$$ $$e\left(\frac{27}{83}\right)$$
$$\chi_{4008}(31,\cdot)$$ 4008.w 166 no $$-1$$ $$1$$ $$e\left(\frac{45}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{113}{166}\right)$$ $$e\left(\frac{70}{83}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{157}{166}\right)$$ $$e\left(\frac{29}{166}\right)$$ $$e\left(\frac{7}{83}\right)$$ $$e\left(\frac{27}{83}\right)$$ $$e\left(\frac{49}{166}\right)$$
$$\chi_{4008}(35,\cdot)$$ 4008.be 166 yes $$-1$$ $$1$$ $$e\left(\frac{119}{166}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{95}{166}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{41}{83}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{161}{166}\right)$$ $$e\left(\frac{36}{83}\right)$$ $$e\left(\frac{44}{83}\right)$$ $$e\left(\frac{3}{166}\right)$$
$$\chi_{4008}(37,\cdot)$$ 4008.s 166 no $$-1$$ $$1$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{30}{83}\right)$$ $$e\left(\frac{131}{166}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{135}{166}\right)$$ $$e\left(\frac{63}{166}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{103}{166}\right)$$ $$e\left(\frac{6}{83}\right)$$
$$\chi_{4008}(41,\cdot)$$ 4008.t 166 no $$1$$ $$1$$ $$e\left(\frac{7}{83}\right)$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{143}{166}\right)$$ $$e\left(\frac{31}{166}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{74}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{14}{83}\right)$$ $$e\left(\frac{25}{166}\right)$$ $$e\left(\frac{49}{83}\right)$$
$$\chi_{4008}(43,\cdot)$$ 4008.u 166 no $$1$$ $$1$$ $$e\left(\frac{2}{83}\right)$$ $$e\left(\frac{57}{166}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{40}{83}\right)$$ $$e\left(\frac{129}{166}\right)$$ $$e\left(\frac{33}{83}\right)$$ $$e\left(\frac{32}{83}\right)$$ $$e\left(\frac{4}{83}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{111}{166}\right)$$
$$\chi_{4008}(47,\cdot)$$ 4008.bc 166 no $$1$$ $$1$$ $$e\left(\frac{49}{166}\right)$$ $$e\left(\frac{55}{166}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{107}{166}\right)$$ $$e\left(\frac{103}{166}\right)$$ $$e\left(\frac{60}{83}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{129}{166}\right)$$ $$e\left(\frac{11}{166}\right)$$
$$\chi_{4008}(49,\cdot)$$ 4008.q 83 no $$1$$ $$1$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{63}{83}\right)$$ $$e\left(\frac{67}{83}\right)$$ $$e\left(\frac{36}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{38}{83}\right)$$ $$e\left(\frac{62}{83}\right)$$ $$e\left(\frac{70}{83}\right)$$ $$e\left(\frac{21}{83}\right)$$ $$e\left(\frac{79}{83}\right)$$
$$\chi_{4008}(53,\cdot)$$ 4008.y 166 yes $$1$$ $$1$$ $$e\left(\frac{109}{166}\right)$$ $$e\left(\frac{40}{83}\right)$$ $$e\left(\frac{32}{83}\right)$$ $$e\left(\frac{11}{83}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{97}{166}\right)$$ $$e\left(\frac{42}{83}\right)$$ $$e\left(\frac{26}{83}\right)$$ $$e\left(\frac{41}{83}\right)$$ $$e\left(\frac{8}{83}\right)$$
$$\chi_{4008}(55,\cdot)$$ 4008.bf 166 no $$1$$ $$1$$ $$e\left(\frac{29}{166}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{165}{166}\right)$$ $$e\left(\frac{43}{166}\right)$$ $$e\left(\frac{105}{166}\right)$$ $$e\left(\frac{66}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{17}{83}\right)$$ $$e\left(\frac{37}{166}\right)$$
$$\chi_{4008}(59,\cdot)$$ 4008.be 166 yes $$-1$$ $$1$$ $$e\left(\frac{113}{166}\right)$$ $$e\left(\frac{137}{166}\right)$$ $$e\left(\frac{93}{166}\right)$$ $$e\left(\frac{51}{83}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{40}{83}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{30}{83}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{127}{166}\right)$$
$$\chi_{4008}(61,\cdot)$$ 4008.bb 166 no $$1$$ $$1$$ $$e\left(\frac{149}{166}\right)$$ $$e\left(\frac{76}{83}\right)$$ $$e\left(\frac{105}{166}\right)$$ $$e\left(\frac{75}{166}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{93}{166}\right)$$ $$e\left(\frac{30}{83}\right)$$ $$e\left(\frac{66}{83}\right)$$ $$e\left(\frac{23}{166}\right)$$ $$e\left(\frac{65}{83}\right)$$
$$\chi_{4008}(65,\cdot)$$ 4008.ba 166 no $$-1$$ $$1$$ $$e\left(\frac{21}{166}\right)$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{7}{166}\right)$$ $$e\left(\frac{44}{83}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{87}{166}\right)$$ $$e\left(\frac{21}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{32}{83}\right)$$
$$\chi_{4008}(67,\cdot)$$ 4008.u 166 no $$1$$ $$1$$ $$e\left(\frac{41}{83}\right)$$ $$e\left(\frac{131}{166}\right)$$ $$e\left(\frac{69}{83}\right)$$ $$e\left(\frac{73}{83}\right)$$ $$e\left(\frac{113}{166}\right)$$ $$e\left(\frac{54}{83}\right)$$ $$e\left(\frac{75}{83}\right)$$ $$e\left(\frac{82}{83}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{159}{166}\right)$$
$$\chi_{4008}(71,\cdot)$$ 4008.v 166 no $$-1$$ $$1$$ $$e\left(\frac{64}{83}\right)$$ $$e\left(\frac{81}{166}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{153}{166}\right)$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{37}{166}\right)$$ $$e\left(\frac{139}{166}\right)$$ $$e\left(\frac{45}{83}\right)$$ $$e\left(\frac{27}{166}\right)$$ $$e\left(\frac{149}{166}\right)$$
$$\chi_{4008}(73,\cdot)$$ 4008.z 166 no $$-1$$ $$1$$ $$e\left(\frac{89}{166}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{1}{83}\right)$$ $$e\left(\frac{37}{166}\right)$$ $$e\left(\frac{69}{166}\right)$$ $$e\left(\frac{8}{83}\right)$$ $$e\left(\frac{13}{166}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{21}{83}\right)$$
$$\chi_{4008}(77,\cdot)$$ 4008.r 166 yes $$-1$$ $$1$$ $$e\left(\frac{73}{83}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{52}{83}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{85}{166}\right)$$ $$e\left(\frac{95}{166}\right)$$ $$e\left(\frac{63}{83}\right)$$ $$e\left(\frac{77}{83}\right)$$ $$e\left(\frac{13}{83}\right)$$
$$\chi_{4008}(79,\cdot)$$ 4008.bf 166 no $$1$$ $$1$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{77}{166}\right)$$ $$e\left(\frac{55}{166}\right)$$ $$e\left(\frac{125}{166}\right)$$ $$e\left(\frac{35}{166}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{65}{83}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{123}{166}\right)$$
$$\chi_{4008}(83,\cdot)$$ 4008.be 166 yes $$-1$$ $$1$$ $$e\left(\frac{43}{166}\right)$$ $$e\left(\frac{11}{166}\right)$$ $$e\left(\frac{125}{166}\right)$$ $$e\left(\frac{15}{83}\right)$$ $$e\left(\frac{19}{83}\right)$$ $$e\left(\frac{2}{83}\right)$$ $$e\left(\frac{107}{166}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{135}{166}\right)$$
$$\chi_{4008}(85,\cdot)$$ 4008.bb 166 no $$1$$ $$1$$ $$e\left(\frac{137}{166}\right)$$ $$e\left(\frac{32}{83}\right)$$ $$e\left(\frac{101}{166}\right)$$ $$e\left(\frac{1}{166}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{61}{166}\right)$$ $$e\left(\frac{17}{83}\right)$$ $$e\left(\frac{54}{83}\right)$$ $$e\left(\frac{49}{166}\right)$$ $$e\left(\frac{23}{83}\right)$$
$$\chi_{4008}(89,\cdot)$$ 4008.ba 166 no $$-1$$ $$1$$ $$e\left(\frac{71}{166}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{46}{83}\right)$$ $$e\left(\frac{111}{166}\right)$$ $$e\left(\frac{67}{83}\right)$$ $$e\left(\frac{57}{166}\right)$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{109}{166}\right)$$ $$e\left(\frac{41}{83}\right)$$
$$\chi_{4008}(91,\cdot)$$ 4008.u 166 no $$1$$ $$1$$ $$e\left(\frac{69}{83}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{23}{83}\right)$$ $$e\left(\frac{52}{83}\right)$$ $$e\left(\frac{93}{166}\right)$$ $$e\left(\frac{18}{83}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{55}{83}\right)$$ $$e\left(\frac{33}{166}\right)$$ $$e\left(\frac{53}{166}\right)$$
$$\chi_{4008}(95,\cdot)$$ 4008.v 166 no $$-1$$ $$1$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{79}{83}\right)$$ $$e\left(\frac{101}{166}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{31}{166}\right)$$ $$e\left(\frac{59}{83}\right)$$ $$e\left(\frac{135}{166}\right)$$ $$e\left(\frac{81}{166}\right)$$