# Properties

 Modulus $6012$ Structure $$C_{498}\times C_{2}\times C_{2}$$ Order $1992$

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(6012)

pari: g = idealstar(,6012,2)

## Character group

 sage: G.order()  pari: g.no Order = 1992 sage: H.invariants()  pari: g.cyc Structure = $$C_{498}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6012}(5,\cdot)$, $\chi_{6012}(3673,\cdot)$, $\chi_{6012}(3007,\cdot)$

## First 32 of 1992 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.

Character Orbit Order Primitive $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$
$$\chi_{6012}(1,\cdot)$$ 6012.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6012}(5,\cdot)$$ 6012.bf 498 no $$1$$ $$1$$ $$e\left(\frac{43}{249}\right)$$ $$e\left(\frac{11}{249}\right)$$ $$e\left(\frac{1}{498}\right)$$ $$e\left(\frac{143}{498}\right)$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{190}{249}\right)$$ $$e\left(\frac{86}{249}\right)$$ $$e\left(\frac{367}{498}\right)$$ $$e\left(\frac{52}{249}\right)$$
$$\chi_{6012}(7,\cdot)$$ 6012.bd 498 yes $$-1$$ $$1$$ $$e\left(\frac{11}{249}\right)$$ $$e\left(\frac{23}{498}\right)$$ $$e\left(\frac{35}{498}\right)$$ $$e\left(\frac{137}{249}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{121}{166}\right)$$ $$e\left(\frac{103}{498}\right)$$ $$e\left(\frac{22}{249}\right)$$ $$e\left(\frac{73}{249}\right)$$ $$e\left(\frac{403}{498}\right)$$
$$\chi_{6012}(11,\cdot)$$ 6012.ba 498 yes $$1$$ $$1$$ $$e\left(\frac{1}{498}\right)$$ $$e\left(\frac{35}{498}\right)$$ $$e\left(\frac{97}{249}\right)$$ $$e\left(\frac{176}{249}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{47}{166}\right)$$ $$e\left(\frac{8}{249}\right)$$ $$e\left(\frac{1}{249}\right)$$ $$e\left(\frac{233}{498}\right)$$ $$e\left(\frac{7}{498}\right)$$
$$\chi_{6012}(13,\cdot)$$ 6012.bc 498 no $$-1$$ $$1$$ $$e\left(\frac{143}{498}\right)$$ $$e\left(\frac{137}{249}\right)$$ $$e\left(\frac{176}{249}\right)$$ $$e\left(\frac{287}{498}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{82}{83}\right)$$ $$e\left(\frac{47}{498}\right)$$ $$e\left(\frac{143}{249}\right)$$ $$e\left(\frac{101}{249}\right)$$ $$e\left(\frac{127}{249}\right)$$
$$\chi_{6012}(17,\cdot)$$ 6012.r 166 no $$1$$ $$1$$ $$e\left(\frac{68}{83}\right)$$ $$e\left(\frac{56}{83}\right)$$ $$e\left(\frac{73}{166}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{61}{83}\right)$$
$$\chi_{6012}(19,\cdot)$$ 6012.t 166 no $$-1$$ $$1$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{121}{166}\right)$$ $$e\left(\frac{47}{166}\right)$$ $$e\left(\frac{82}{83}\right)$$ $$e\left(\frac{43}{83}\right)$$ $$e\left(\frac{127}{166}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{34}{83}\right)$$ $$e\left(\frac{157}{166}\right)$$
$$\chi_{6012}(23,\cdot)$$ 6012.be 498 yes $$-1$$ $$1$$ $$e\left(\frac{190}{249}\right)$$ $$e\left(\frac{103}{498}\right)$$ $$e\left(\frac{8}{249}\right)$$ $$e\left(\frac{47}{498}\right)$$ $$e\left(\frac{9}{83}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{353}{498}\right)$$ $$e\left(\frac{131}{249}\right)$$ $$e\left(\frac{145}{498}\right)$$ $$e\left(\frac{419}{498}\right)$$
$$\chi_{6012}(25,\cdot)$$ 6012.y 249 no $$1$$ $$1$$ $$e\left(\frac{86}{249}\right)$$ $$e\left(\frac{22}{249}\right)$$ $$e\left(\frac{1}{249}\right)$$ $$e\left(\frac{143}{249}\right)$$ $$e\left(\frac{53}{83}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{131}{249}\right)$$ $$e\left(\frac{172}{249}\right)$$ $$e\left(\frac{118}{249}\right)$$ $$e\left(\frac{104}{249}\right)$$
$$\chi_{6012}(29,\cdot)$$ 6012.bb 498 no $$-1$$ $$1$$ $$e\left(\frac{367}{498}\right)$$ $$e\left(\frac{73}{249}\right)$$ $$e\left(\frac{233}{498}\right)$$ $$e\left(\frac{101}{249}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{34}{83}\right)$$ $$e\left(\frac{145}{498}\right)$$ $$e\left(\frac{118}{249}\right)$$ $$e\left(\frac{353}{498}\right)$$ $$e\left(\frac{164}{249}\right)$$
$$\chi_{6012}(31,\cdot)$$ 6012.bd 498 yes $$-1$$ $$1$$ $$e\left(\frac{52}{249}\right)$$ $$e\left(\frac{403}{498}\right)$$ $$e\left(\frac{7}{498}\right)$$ $$e\left(\frac{127}{249}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{157}{166}\right)$$ $$e\left(\frac{419}{498}\right)$$ $$e\left(\frac{104}{249}\right)$$ $$e\left(\frac{164}{249}\right)$$ $$e\left(\frac{479}{498}\right)$$
$$\chi_{6012}(35,\cdot)$$ 6012.s 166 no $$-1$$ $$1$$ $$e\left(\frac{18}{83}\right)$$ $$e\left(\frac{15}{166}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{139}{166}\right)$$ $$e\left(\frac{41}{83}\right)$$ $$e\left(\frac{13}{166}\right)$$ $$e\left(\frac{161}{166}\right)$$ $$e\left(\frac{36}{83}\right)$$ $$e\left(\frac{5}{166}\right)$$ $$e\left(\frac{3}{166}\right)$$
$$\chi_{6012}(37,\cdot)$$ 6012.u 166 no $$-1$$ $$1$$ $$e\left(\frac{61}{166}\right)$$ $$e\left(\frac{30}{83}\right)$$ $$e\left(\frac{24}{83}\right)$$ $$e\left(\frac{141}{166}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{26}{83}\right)$$ $$e\left(\frac{63}{166}\right)$$ $$e\left(\frac{61}{83}\right)$$ $$e\left(\frac{10}{83}\right)$$ $$e\left(\frac{6}{83}\right)$$
$$\chi_{6012}(41,\cdot)$$ 6012.bf 498 no $$1$$ $$1$$ $$e\left(\frac{187}{249}\right)$$ $$e\left(\frac{71}{249}\right)$$ $$e\left(\frac{97}{498}\right)$$ $$e\left(\frac{425}{498}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{74}{83}\right)$$ $$e\left(\frac{4}{249}\right)$$ $$e\left(\frac{125}{249}\right)$$ $$e\left(\frac{241}{498}\right)$$ $$e\left(\frac{64}{249}\right)$$
$$\chi_{6012}(43,\cdot)$$ 6012.z 498 yes $$1$$ $$1$$ $$e\left(\frac{427}{498}\right)$$ $$e\left(\frac{5}{498}\right)$$ $$e\left(\frac{419}{498}\right)$$ $$e\left(\frac{157}{498}\right)$$ $$e\left(\frac{129}{166}\right)$$ $$e\left(\frac{149}{166}\right)$$ $$e\left(\frac{179}{249}\right)$$ $$e\left(\frac{178}{249}\right)$$ $$e\left(\frac{70}{249}\right)$$ $$e\left(\frac{1}{498}\right)$$
$$\chi_{6012}(47,\cdot)$$ 6012.ba 498 yes $$1$$ $$1$$ $$e\left(\frac{313}{498}\right)$$ $$e\left(\frac{497}{498}\right)$$ $$e\left(\frac{232}{249}\right)$$ $$e\left(\frac{59}{249}\right)$$ $$e\left(\frac{107}{166}\right)$$ $$e\left(\frac{103}{166}\right)$$ $$e\left(\frac{14}{249}\right)$$ $$e\left(\frac{64}{249}\right)$$ $$e\left(\frac{221}{498}\right)$$ $$e\left(\frac{199}{498}\right)$$
$$\chi_{6012}(49,\cdot)$$ 6012.y 249 no $$1$$ $$1$$ $$e\left(\frac{22}{249}\right)$$ $$e\left(\frac{23}{249}\right)$$ $$e\left(\frac{35}{249}\right)$$ $$e\left(\frac{25}{249}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{38}{83}\right)$$ $$e\left(\frac{103}{249}\right)$$ $$e\left(\frac{44}{249}\right)$$ $$e\left(\frac{146}{249}\right)$$ $$e\left(\frac{154}{249}\right)$$
$$\chi_{6012}(53,\cdot)$$ 6012.r 166 no $$1$$ $$1$$ $$e\left(\frac{13}{83}\right)$$ $$e\left(\frac{40}{83}\right)$$ $$e\left(\frac{147}{166}\right)$$ $$e\left(\frac{105}{166}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{7}{83}\right)$$ $$e\left(\frac{42}{83}\right)$$ $$e\left(\frac{26}{83}\right)$$ $$e\left(\frac{165}{166}\right)$$ $$e\left(\frac{8}{83}\right)$$
$$\chi_{6012}(55,\cdot)$$ 6012.x 166 no $$1$$ $$1$$ $$e\left(\frac{29}{166}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{65}{166}\right)$$ $$e\left(\frac{165}{166}\right)$$ $$e\left(\frac{43}{166}\right)$$ $$e\left(\frac{105}{166}\right)$$ $$e\left(\frac{66}{83}\right)$$ $$e\left(\frac{29}{83}\right)$$ $$e\left(\frac{17}{83}\right)$$ $$e\left(\frac{37}{166}\right)$$
$$\chi_{6012}(59,\cdot)$$ 6012.be 498 yes $$-1$$ $$1$$ $$e\left(\frac{211}{249}\right)$$ $$e\left(\frac{79}{498}\right)$$ $$e\left(\frac{98}{249}\right)$$ $$e\left(\frac{389}{498}\right)$$ $$e\left(\frac{48}{83}\right)$$ $$e\left(\frac{163}{166}\right)$$ $$e\left(\frac{29}{498}\right)$$ $$e\left(\frac{173}{249}\right)$$ $$e\left(\frac{469}{498}\right)$$ $$e\left(\frac{215}{498}\right)$$
$$\chi_{6012}(61,\cdot)$$ 6012.y 249 no $$1$$ $$1$$ $$e\left(\frac{182}{249}\right)$$ $$e\left(\frac{145}{249}\right)$$ $$e\left(\frac{199}{249}\right)$$ $$e\left(\frac{71}{249}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{5}{83}\right)$$ $$e\left(\frac{173}{249}\right)$$ $$e\left(\frac{115}{249}\right)$$ $$e\left(\frac{76}{249}\right)$$ $$e\left(\frac{29}{249}\right)$$
$$\chi_{6012}(65,\cdot)$$ 6012.bb 498 no $$-1$$ $$1$$ $$e\left(\frac{229}{498}\right)$$ $$e\left(\frac{148}{249}\right)$$ $$e\left(\frac{353}{498}\right)$$ $$e\left(\frac{215}{249}\right)$$ $$e\left(\frac{117}{166}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{427}{498}\right)$$ $$e\left(\frac{229}{249}\right)$$ $$e\left(\frac{71}{498}\right)$$ $$e\left(\frac{179}{249}\right)$$
$$\chi_{6012}(67,\cdot)$$ 6012.z 498 yes $$1$$ $$1$$ $$e\left(\frac{329}{498}\right)$$ $$e\left(\frac{61}{498}\right)$$ $$e\left(\frac{331}{498}\right)$$ $$e\left(\frac{23}{498}\right)$$ $$e\left(\frac{113}{166}\right)$$ $$e\left(\frac{25}{166}\right)$$ $$e\left(\frac{142}{249}\right)$$ $$e\left(\frac{80}{249}\right)$$ $$e\left(\frac{107}{249}\right)$$ $$e\left(\frac{311}{498}\right)$$
$$\chi_{6012}(71,\cdot)$$ 6012.s 166 no $$-1$$ $$1$$ $$e\left(\frac{64}{83}\right)$$ $$e\left(\frac{81}{166}\right)$$ $$e\left(\frac{49}{83}\right)$$ $$e\left(\frac{153}{166}\right)$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{37}{166}\right)$$ $$e\left(\frac{139}{166}\right)$$ $$e\left(\frac{45}{83}\right)$$ $$e\left(\frac{27}{166}\right)$$ $$e\left(\frac{149}{166}\right)$$
$$\chi_{6012}(73,\cdot)$$ 6012.u 166 no $$-1$$ $$1$$ $$e\left(\frac{89}{166}\right)$$ $$e\left(\frac{22}{83}\right)$$ $$e\left(\frac{1}{83}\right)$$ $$e\left(\frac{37}{166}\right)$$ $$e\left(\frac{69}{166}\right)$$ $$e\left(\frac{8}{83}\right)$$ $$e\left(\frac{13}{166}\right)$$ $$e\left(\frac{6}{83}\right)$$ $$e\left(\frac{35}{83}\right)$$ $$e\left(\frac{21}{83}\right)$$
$$\chi_{6012}(77,\cdot)$$ 6012.bb 498 no $$-1$$ $$1$$ $$e\left(\frac{23}{498}\right)$$ $$e\left(\frac{29}{249}\right)$$ $$e\left(\frac{229}{498}\right)$$ $$e\left(\frac{64}{249}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{1}{83}\right)$$ $$e\left(\frac{119}{498}\right)$$ $$e\left(\frac{23}{249}\right)$$ $$e\left(\frac{379}{498}\right)$$ $$e\left(\frac{205}{249}\right)$$
$$\chi_{6012}(79,\cdot)$$ 6012.z 498 yes $$1$$ $$1$$ $$e\left(\frac{361}{498}\right)$$ $$e\left(\frac{185}{498}\right)$$ $$e\left(\frac{65}{498}\right)$$ $$e\left(\frac{331}{498}\right)$$ $$e\left(\frac{125}{166}\right)$$ $$e\left(\frac{35}{166}\right)$$ $$e\left(\frac{149}{249}\right)$$ $$e\left(\frac{112}{249}\right)$$ $$e\left(\frac{100}{249}\right)$$ $$e\left(\frac{37}{498}\right)$$
$$\chi_{6012}(83,\cdot)$$ 6012.be 498 yes $$-1$$ $$1$$ $$e\left(\frac{23}{249}\right)$$ $$e\left(\frac{365}{498}\right)$$ $$e\left(\frac{229}{249}\right)$$ $$e\left(\frac{7}{498}\right)$$ $$e\left(\frac{19}{83}\right)$$ $$e\left(\frac{87}{166}\right)$$ $$e\left(\frac{487}{498}\right)$$ $$e\left(\frac{46}{249}\right)$$ $$e\left(\frac{11}{498}\right)$$ $$e\left(\frac{73}{498}\right)$$
$$\chi_{6012}(85,\cdot)$$ 6012.y 249 no $$1$$ $$1$$ $$e\left(\frac{247}{249}\right)$$ $$e\left(\frac{179}{249}\right)$$ $$e\left(\frac{110}{249}\right)$$ $$e\left(\frac{43}{249}\right)$$ $$e\left(\frac{20}{83}\right)$$ $$e\left(\frac{72}{83}\right)$$ $$e\left(\frac{217}{249}\right)$$ $$e\left(\frac{245}{249}\right)$$ $$e\left(\frac{32}{249}\right)$$ $$e\left(\frac{235}{249}\right)$$
$$\chi_{6012}(89,\cdot)$$ 6012.v 166 no $$-1$$ $$1$$ $$e\left(\frac{71}{166}\right)$$ $$e\left(\frac{39}{83}\right)$$ $$e\left(\frac{79}{166}\right)$$ $$e\left(\frac{46}{83}\right)$$ $$e\left(\frac{111}{166}\right)$$ $$e\left(\frac{67}{83}\right)$$ $$e\left(\frac{57}{166}\right)$$ $$e\left(\frac{71}{83}\right)$$ $$e\left(\frac{109}{166}\right)$$ $$e\left(\frac{41}{83}\right)$$
$$\chi_{6012}(91,\cdot)$$ 6012.x 166 no $$1$$ $$1$$ $$e\left(\frac{55}{166}\right)$$ $$e\left(\frac{99}{166}\right)$$ $$e\left(\frac{129}{166}\right)$$ $$e\left(\frac{21}{166}\right)$$ $$e\left(\frac{93}{166}\right)$$ $$e\left(\frac{119}{166}\right)$$ $$e\left(\frac{25}{83}\right)$$ $$e\left(\frac{55}{83}\right)$$ $$e\left(\frac{58}{83}\right)$$ $$e\left(\frac{53}{166}\right)$$
$$\chi_{6012}(95,\cdot)$$ 6012.be 498 yes $$-1$$ $$1$$ $$e\left(\frac{130}{249}\right)$$ $$e\left(\frac{385}{498}\right)$$ $$e\left(\frac{71}{249}\right)$$ $$e\left(\frac{137}{498}\right)$$ $$e\left(\frac{28}{83}\right)$$ $$e\left(\frac{19}{166}\right)$$ $$e\left(\frac{425}{498}\right)$$ $$e\left(\frac{11}{249}\right)$$ $$e\left(\frac{73}{498}\right)$$ $$e\left(\frac{77}{498}\right)$$