# Properties

 Modulus 6018 Structure $$C_{464}\times C_{2}\times C_{2}$$ Order 1856

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(6018)

pari: g = idealstar(,6018,2)

## Character group

 sage: G.order()  pari: g.no Order = 1856 sage: H.invariants()  pari: g.cyc Structure = $$C_{464}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6018}(2539,\cdot)$, $\chi_{6018}(2005,\cdot)$, $\chi_{6018}(4013,\cdot)$

## First 32 of 1856 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 19 23 25 29 31 35
$$\chi_{6018}(1,\cdot)$$ 6018.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6018}(5,\cdot)$$ 6018.bn 464 No $$1$$ $$1$$ $$e\left(\frac{317}{464}\right)$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{127}{464}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{343}{464}\right)$$ $$e\left(\frac{85}{232}\right)$$ $$e\left(\frac{213}{464}\right)$$ $$e\left(\frac{409}{464}\right)$$ $$e\left(\frac{57}{58}\right)$$
$$\chi_{6018}(7,\cdot)$$ 6018.bl 464 No $$-1$$ $$1$$ $$e\left(\frac{139}{464}\right)$$ $$e\left(\frac{69}{464}\right)$$ $$e\left(\frac{265}{464}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{97}{232}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{291}{464}\right)$$ $$e\left(\frac{183}{464}\right)$$ $$e\left(\frac{13}{29}\right)$$
$$\chi_{6018}(11,\cdot)$$ 6018.bm 464 No $$-1$$ $$1$$ $$e\left(\frac{127}{464}\right)$$ $$e\left(\frac{265}{464}\right)$$ $$e\left(\frac{157}{464}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{117}{232}\right)$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{127}{232}\right)$$ $$e\left(\frac{119}{464}\right)$$ $$e\left(\frac{27}{464}\right)$$ $$e\left(\frac{49}{58}\right)$$
$$\chi_{6018}(13,\cdot)$$ 6018.be 116 No $$-1$$ $$1$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{18}{29}\right)$$
$$\chi_{6018}(19,\cdot)$$ 6018.bi 232 No $$1$$ $$1$$ $$e\left(\frac{71}{232}\right)$$ $$e\left(\frac{97}{232}\right)$$ $$e\left(\frac{117}{232}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{221}{232}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{167}{232}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{21}{29}\right)$$
$$\chi_{6018}(23,\cdot)$$ 6018.bm 464 No $$-1$$ $$1$$ $$e\left(\frac{343}{464}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{45}{116}\right)$$ $$e\left(\frac{221}{232}\right)$$ $$e\left(\frac{205}{464}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{431}{464}\right)$$ $$e\left(\frac{51}{464}\right)$$ $$e\left(\frac{41}{58}\right)$$
$$\chi_{6018}(25,\cdot)$$ 6018.bi 232 No $$1$$ $$1$$ $$e\left(\frac{85}{232}\right)$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{127}{232}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{111}{232}\right)$$ $$e\left(\frac{85}{116}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{177}{232}\right)$$ $$e\left(\frac{28}{29}\right)$$
$$\chi_{6018}(29,\cdot)$$ 6018.bn 464 No $$1$$ $$1$$ $$e\left(\frac{213}{464}\right)$$ $$e\left(\frac{291}{464}\right)$$ $$e\left(\frac{119}{464}\right)$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{167}{232}\right)$$ $$e\left(\frac{431}{464}\right)$$ $$e\left(\frac{213}{232}\right)$$ $$e\left(\frac{269}{464}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{5}{58}\right)$$
$$\chi_{6018}(31,\cdot)$$ 6018.bk 464 No $$1$$ $$1$$ $$e\left(\frac{409}{464}\right)$$ $$e\left(\frac{183}{464}\right)$$ $$e\left(\frac{27}{464}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{51}{464}\right)$$ $$e\left(\frac{177}{232}\right)$$ $$e\left(\frac{449}{464}\right)$$ $$e\left(\frac{213}{464}\right)$$ $$e\left(\frac{8}{29}\right)$$
$$\chi_{6018}(35,\cdot)$$ 6018.z 58 No $$-1$$ $$1$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{13}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{21}{29}\right)$$ $$e\left(\frac{41}{58}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{5}{58}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{25}{58}\right)$$
$$\chi_{6018}(37,\cdot)$$ 6018.bk 464 No $$1$$ $$1$$ $$e\left(\frac{1}{464}\right)$$ $$e\left(\frac{351}{464}\right)$$ $$e\left(\frac{67}{464}\right)$$ $$e\left(\frac{107}{116}\right)$$ $$e\left(\frac{211}{232}\right)$$ $$e\left(\frac{75}{464}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{169}{464}\right)$$ $$e\left(\frac{13}{464}\right)$$ $$e\left(\frac{22}{29}\right)$$
$$\chi_{6018}(41,\cdot)$$ 6018.bn 464 No $$1$$ $$1$$ $$e\left(\frac{179}{464}\right)$$ $$e\left(\frac{421}{464}\right)$$ $$e\left(\frac{161}{464}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{185}{232}\right)$$ $$e\left(\frac{201}{464}\right)$$ $$e\left(\frac{179}{232}\right)$$ $$e\left(\frac{91}{464}\right)$$ $$e\left(\frac{7}{464}\right)$$ $$e\left(\frac{17}{58}\right)$$
$$\chi_{6018}(43,\cdot)$$ 6018.bg 232 No $$-1$$ $$1$$ $$e\left(\frac{9}{232}\right)$$ $$e\left(\frac{143}{232}\right)$$ $$e\left(\frac{23}{232}\right)$$ $$e\left(\frac{3}{29}\right)$$ $$e\left(\frac{43}{116}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{9}{116}\right)$$ $$e\left(\frac{129}{232}\right)$$ $$e\left(\frac{1}{232}\right)$$ $$e\left(\frac{19}{29}\right)$$
$$\chi_{6018}(47,\cdot)$$ 6018.bf 116 No $$1$$ $$1$$ $$e\left(\frac{15}{116}\right)$$ $$e\left(\frac{103}{116}\right)$$ $$e\left(\frac{19}{116}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{15}{58}\right)$$ $$e\left(\frac{99}{116}\right)$$ $$e\left(\frac{79}{116}\right)$$ $$e\left(\frac{1}{58}\right)$$
$$\chi_{6018}(49,\cdot)$$ 6018.bi 232 No $$1$$ $$1$$ $$e\left(\frac{139}{232}\right)$$ $$e\left(\frac{69}{232}\right)$$ $$e\left(\frac{33}{232}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{97}{116}\right)$$ $$e\left(\frac{217}{232}\right)$$ $$e\left(\frac{23}{116}\right)$$ $$e\left(\frac{59}{232}\right)$$ $$e\left(\frac{183}{232}\right)$$ $$e\left(\frac{26}{29}\right)$$
$$\chi_{6018}(53,\cdot)$$ 6018.bj 232 No $$-1$$ $$1$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{25}{232}\right)$$ $$e\left(\frac{33}{58}\right)$$ $$e\left(\frac{77}{116}\right)$$ $$e\left(\frac{73}{232}\right)$$ $$e\left(\frac{35}{116}\right)$$ $$e\left(\frac{115}{232}\right)$$ $$e\left(\frac{107}{232}\right)$$ $$e\left(\frac{35}{58}\right)$$
$$\chi_{6018}(55,\cdot)$$ 6018.be 116 No $$-1$$ $$1$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{101}{116}\right)$$ $$e\left(\frac{71}{116}\right)$$ $$e\left(\frac{3}{58}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{31}{116}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{24}{29}\right)$$
$$\chi_{6018}(61,\cdot)$$ 6018.bk 464 No $$1$$ $$1$$ $$e\left(\frac{19}{464}\right)$$ $$e\left(\frac{173}{464}\right)$$ $$e\left(\frac{345}{464}\right)$$ $$e\left(\frac{61}{116}\right)$$ $$e\left(\frac{65}{232}\right)$$ $$e\left(\frac{33}{464}\right)$$ $$e\left(\frac{19}{232}\right)$$ $$e\left(\frac{427}{464}\right)$$ $$e\left(\frac{247}{464}\right)$$ $$e\left(\frac{12}{29}\right)$$
$$\chi_{6018}(65,\cdot)$$ 6018.bm 464 No $$-1$$ $$1$$ $$e\left(\frac{273}{464}\right)$$ $$e\left(\frac{7}{464}\right)$$ $$e\left(\frac{195}{464}\right)$$ $$e\left(\frac{95}{116}\right)$$ $$e\left(\frac{67}{232}\right)$$ $$e\left(\frac{59}{464}\right)$$ $$e\left(\frac{41}{232}\right)$$ $$e\left(\frac{201}{464}\right)$$ $$e\left(\frac{69}{464}\right)$$ $$e\left(\frac{35}{58}\right)$$
$$\chi_{6018}(67,\cdot)$$ 6018.ba 58 No $$-1$$ $$1$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{25}{58}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{19}{58}\right)$$ $$e\left(\frac{28}{29}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{7}{29}\right)$$
$$\chi_{6018}(71,\cdot)$$ 6018.bn 464 No $$1$$ $$1$$ $$e\left(\frac{89}{464}\right)$$ $$e\left(\frac{383}{464}\right)$$ $$e\left(\frac{163}{464}\right)$$ $$e\left(\frac{69}{116}\right)$$ $$e\left(\frac{219}{232}\right)$$ $$e\left(\frac{411}{464}\right)$$ $$e\left(\frac{89}{232}\right)$$ $$e\left(\frac{193}{464}\right)$$ $$e\left(\frac{229}{464}\right)$$ $$e\left(\frac{1}{58}\right)$$
$$\chi_{6018}(73,\cdot)$$ 6018.bk 464 No $$1$$ $$1$$ $$e\left(\frac{245}{464}\right)$$ $$e\left(\frac{155}{464}\right)$$ $$e\left(\frac{175}{464}\right)$$ $$e\left(\frac{115}{116}\right)$$ $$e\left(\frac{191}{232}\right)$$ $$e\left(\frac{279}{464}\right)$$ $$e\left(\frac{13}{232}\right)$$ $$e\left(\frac{109}{464}\right)$$ $$e\left(\frac{401}{464}\right)$$ $$e\left(\frac{25}{29}\right)$$
$$\chi_{6018}(77,\cdot)$$ 6018.bh 232 No $$1$$ $$1$$ $$e\left(\frac{133}{232}\right)$$ $$e\left(\frac{167}{232}\right)$$ $$e\left(\frac{211}{232}\right)$$ $$e\left(\frac{25}{29}\right)$$ $$e\left(\frac{107}{116}\right)$$ $$e\left(\frac{115}{232}\right)$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{205}{232}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{17}{58}\right)$$
$$\chi_{6018}(79,\cdot)$$ 6018.bl 464 No $$-1$$ $$1$$ $$e\left(\frac{7}{464}\right)$$ $$e\left(\frac{137}{464}\right)$$ $$e\left(\frac{237}{464}\right)$$ $$e\left(\frac{111}{116}\right)$$ $$e\left(\frac{85}{232}\right)$$ $$e\left(\frac{293}{464}\right)$$ $$e\left(\frac{7}{232}\right)$$ $$e\left(\frac{255}{464}\right)$$ $$e\left(\frac{323}{464}\right)$$ $$e\left(\frac{9}{29}\right)$$
$$\chi_{6018}(83,\cdot)$$ 6018.bh 232 No $$1$$ $$1$$ $$e\left(\frac{199}{232}\right)$$ $$e\left(\frac{133}{232}\right)$$ $$e\left(\frac{225}{232}\right)$$ $$e\left(\frac{18}{29}\right)$$ $$e\left(\frac{113}{116}\right)$$ $$e\left(\frac{193}{232}\right)$$ $$e\left(\frac{83}{116}\right)$$ $$e\left(\frac{223}{232}\right)$$ $$e\left(\frac{35}{232}\right)$$ $$e\left(\frac{25}{58}\right)$$
$$\chi_{6018}(89,\cdot)$$ 6018.bf 116 No $$1$$ $$1$$ $$e\left(\frac{17}{116}\right)$$ $$e\left(\frac{109}{116}\right)$$ $$e\left(\frac{37}{116}\right)$$ $$e\left(\frac{13}{58}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{57}{116}\right)$$ $$e\left(\frac{17}{58}\right)$$ $$e\left(\frac{89}{116}\right)$$ $$e\left(\frac{105}{116}\right)$$ $$e\left(\frac{5}{58}\right)$$
$$\chi_{6018}(91,\cdot)$$ 6018.bk 464 No $$1$$ $$1$$ $$e\left(\frac{95}{464}\right)$$ $$e\left(\frac{401}{464}\right)$$ $$e\left(\frac{333}{464}\right)$$ $$e\left(\frac{73}{116}\right)$$ $$e\left(\frac{93}{232}\right)$$ $$e\left(\frac{165}{464}\right)$$ $$e\left(\frac{95}{232}\right)$$ $$e\left(\frac{279}{464}\right)$$ $$e\left(\frac{307}{464}\right)$$ $$e\left(\frac{2}{29}\right)$$
$$\chi_{6018}(95,\cdot)$$ 6018.bn 464 No $$1$$ $$1$$ $$e\left(\frac{459}{464}\right)$$ $$e\left(\frac{333}{464}\right)$$ $$e\left(\frac{361}{464}\right)$$ $$e\left(\frac{103}{116}\right)$$ $$e\left(\frac{105}{232}\right)$$ $$e\left(\frac{321}{464}\right)$$ $$e\left(\frac{227}{232}\right)$$ $$e\left(\frac{83}{464}\right)$$ $$e\left(\frac{399}{464}\right)$$ $$e\left(\frac{41}{58}\right)$$
$$\chi_{6018}(97,\cdot)$$ 6018.bk 464 No $$1$$ $$1$$ $$e\left(\frac{45}{464}\right)$$ $$e\left(\frac{19}{464}\right)$$ $$e\left(\frac{231}{464}\right)$$ $$e\left(\frac{59}{116}\right)$$ $$e\left(\frac{215}{232}\right)$$ $$e\left(\frac{127}{464}\right)$$ $$e\left(\frac{45}{232}\right)$$ $$e\left(\frac{181}{464}\right)$$ $$e\left(\frac{121}{464}\right)$$ $$e\left(\frac{4}{29}\right)$$
$$\chi_{6018}(101,\cdot)$$ 6018.x 58 No $$1$$ $$1$$ $$e\left(\frac{4}{29}\right)$$ $$e\left(\frac{53}{58}\right)$$ $$e\left(\frac{43}{58}\right)$$ $$e\left(\frac{31}{58}\right)$$ $$e\left(\frac{6}{29}\right)$$ $$e\left(\frac{49}{58}\right)$$ $$e\left(\frac{8}{29}\right)$$ $$e\left(\frac{9}{29}\right)$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{3}{58}\right)$$
$$\chi_{6018}(103,\cdot)$$ 6018.v 58 No $$-1$$ $$1$$ $$e\left(\frac{23}{29}\right)$$ $$e\left(\frac{11}{29}\right)$$ $$e\left(\frac{37}{58}\right)$$ $$e\left(\frac{55}{58}\right)$$ $$e\left(\frac{20}{29}\right)$$ $$e\left(\frac{57}{58}\right)$$ $$e\left(\frac{17}{29}\right)$$ $$e\left(\frac{1}{29}\right)$$ $$e\left(\frac{47}{58}\right)$$ $$e\left(\frac{5}{29}\right)$$