Properties

 Modulus 6027 Structure $$C_{840}\times C_{2}\times C_{2}$$ Order 3360

Show commands for: SageMath / Pari/GP

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

sage: H = DirichletGroup_conrey(6027)

pari: g = idealstar(,6027,2)

Character group

 sage: G.order()  pari: g.no Order = 3360 sage: H.invariants()  pari: g.cyc Structure = $$C_{840}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6027}(5050,\cdot)$, $\chi_{6027}(2008,\cdot)$, $\chi_{6027}(4019,\cdot)$

First 32 of 3360 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 2 4 5 8 10 11 13 16 17 19
$$\chi_{6027}(1,\cdot)$$ 6027.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6027}(2,\cdot)$$ 6027.eq 420 Yes $$-1$$ $$1$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{89}{420}\right)$$ $$e\left(\frac{81}{140}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{179}{420}\right)$$ $$e\left(\frac{31}{60}\right)$$
$$\chi_{6027}(4,\cdot)$$ 6027.ef 210 No $$1$$ $$1$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{89}{210}\right)$$ $$e\left(\frac{11}{70}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{1}{30}\right)$$
$$\chi_{6027}(5,\cdot)$$ 6027.er 420 Yes $$1$$ $$1$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{79}{210}\right)$$ $$e\left(\frac{323}{420}\right)$$ $$e\left(\frac{117}{140}\right)$$ $$e\left(\frac{1}{105}\right)$$ $$e\left(\frac{383}{420}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{6027}(8,\cdot)$$ 6027.ea 140 Yes $$-1$$ $$1$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{9}{35}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{103}{140}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{39}{140}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{6027}(10,\cdot)$$ 6027.eg 210 No $$-1$$ $$1$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{79}{210}\right)$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{131}{210}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{71}{210}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{6027}(11,\cdot)$$ 6027.eu 840 Yes $$1$$ $$1$$ $$e\left(\frac{89}{420}\right)$$ $$e\left(\frac{89}{210}\right)$$ $$e\left(\frac{323}{420}\right)$$ $$e\left(\frac{89}{140}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{689}{840}\right)$$ $$e\left(\frac{211}{280}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{659}{840}\right)$$ $$e\left(\frac{1}{120}\right)$$
$$\chi_{6027}(13,\cdot)$$ 6027.em 280 No $$1$$ $$1$$ $$e\left(\frac{81}{140}\right)$$ $$e\left(\frac{11}{70}\right)$$ $$e\left(\frac{117}{140}\right)$$ $$e\left(\frac{103}{140}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{211}{280}\right)$$ $$e\left(\frac{267}{280}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{61}{280}\right)$$ $$e\left(\frac{19}{40}\right)$$
$$\chi_{6027}(16,\cdot)$$ 6027.ds 105 No $$1$$ $$1$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{1}{105}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{104}{105}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{11}{35}\right)$$ $$e\left(\frac{97}{105}\right)$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{6027}(17,\cdot)$$ 6027.ew 840 Yes $$-1$$ $$1$$ $$e\left(\frac{179}{420}\right)$$ $$e\left(\frac{179}{210}\right)$$ $$e\left(\frac{383}{420}\right)$$ $$e\left(\frac{39}{140}\right)$$ $$e\left(\frac{71}{210}\right)$$ $$e\left(\frac{659}{840}\right)$$ $$e\left(\frac{61}{280}\right)$$ $$e\left(\frac{74}{105}\right)$$ $$e\left(\frac{509}{840}\right)$$ $$e\left(\frac{31}{120}\right)$$
$$\chi_{6027}(19,\cdot)$$ 6027.dt 120 No $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{120}\right)$$ $$e\left(\frac{19}{40}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{31}{120}\right)$$ $$e\left(\frac{23}{120}\right)$$
$$\chi_{6027}(20,\cdot)$$ 6027.dz 140 Yes $$1$$ $$1$$ $$e\left(\frac{26}{35}\right)$$ $$e\left(\frac{17}{35}\right)$$ $$e\left(\frac{9}{70}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{61}{70}\right)$$ $$e\left(\frac{27}{140}\right)$$ $$e\left(\frac{139}{140}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{107}{140}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{6027}(22,\cdot)$$ 6027.eo 280 No $$-1$$ $$1$$ $$e\left(\frac{99}{140}\right)$$ $$e\left(\frac{29}{70}\right)$$ $$e\left(\frac{73}{140}\right)$$ $$e\left(\frac{17}{140}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{9}{280}\right)$$ $$e\left(\frac{93}{280}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{59}{280}\right)$$ $$e\left(\frac{21}{40}\right)$$
$$\chi_{6027}(23,\cdot)$$ 6027.ek 210 Yes $$-1$$ $$1$$ $$e\left(\frac{89}{210}\right)$$ $$e\left(\frac{89}{105}\right)$$ $$e\left(\frac{113}{210}\right)$$ $$e\left(\frac{19}{70}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{41}{105}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{86}{105}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{6027}(25,\cdot)$$ 6027.ef 210 No $$1$$ $$1$$ $$e\left(\frac{53}{105}\right)$$ $$e\left(\frac{1}{105}\right)$$ $$e\left(\frac{26}{105}\right)$$ $$e\left(\frac{18}{35}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{113}{210}\right)$$ $$e\left(\frac{47}{70}\right)$$ $$e\left(\frac{2}{105}\right)$$ $$e\left(\frac{173}{210}\right)$$ $$e\left(\frac{7}{30}\right)$$
$$\chi_{6027}(26,\cdot)$$ 6027.ew 840 Yes $$-1$$ $$1$$ $$e\left(\frac{31}{420}\right)$$ $$e\left(\frac{31}{210}\right)$$ $$e\left(\frac{247}{420}\right)$$ $$e\left(\frac{31}{140}\right)$$ $$e\left(\frac{139}{210}\right)$$ $$e\left(\frac{811}{840}\right)$$ $$e\left(\frac{149}{280}\right)$$ $$e\left(\frac{31}{105}\right)$$ $$e\left(\frac{541}{840}\right)$$ $$e\left(\frac{119}{120}\right)$$
$$\chi_{6027}(29,\cdot)$$ 6027.ep 280 Yes $$1$$ $$1$$ $$e\left(\frac{27}{140}\right)$$ $$e\left(\frac{27}{70}\right)$$ $$e\left(\frac{109}{140}\right)$$ $$e\left(\frac{81}{140}\right)$$ $$e\left(\frac{34}{35}\right)$$ $$e\left(\frac{47}{280}\right)$$ $$e\left(\frac{159}{280}\right)$$ $$e\left(\frac{27}{35}\right)$$ $$e\left(\frac{277}{280}\right)$$ $$e\left(\frac{23}{40}\right)$$
$$\chi_{6027}(31,\cdot)$$ 6027.ck 30 No $$-1$$ $$1$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{6027}(32,\cdot)$$ 6027.dr 84 Yes $$-1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{5}{84}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{6027}(34,\cdot)$$ 6027.em 280 No $$1$$ $$1$$ $$e\left(\frac{129}{140}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{93}{140}\right)$$ $$e\left(\frac{107}{140}\right)$$ $$e\left(\frac{41}{70}\right)$$ $$e\left(\frac{279}{280}\right)$$ $$e\left(\frac{223}{280}\right)$$ $$e\left(\frac{24}{35}\right)$$ $$e\left(\frac{9}{280}\right)$$ $$e\left(\frac{31}{40}\right)$$
$$\chi_{6027}(37,\cdot)$$ 6027.ds 105 No $$1$$ $$1$$ $$e\left(\frac{64}{105}\right)$$ $$e\left(\frac{23}{105}\right)$$ $$e\left(\frac{73}{105}\right)$$ $$e\left(\frac{29}{35}\right)$$ $$e\left(\frac{32}{105}\right)$$ $$e\left(\frac{92}{105}\right)$$ $$e\left(\frac{33}{35}\right)$$ $$e\left(\frac{46}{105}\right)$$ $$e\left(\frac{47}{105}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{6027}(38,\cdot)$$ 6027.ec 168 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{84}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{73}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{37}{168}\right)$$ $$e\left(\frac{3}{56}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{115}{168}\right)$$ $$e\left(\frac{17}{24}\right)$$
$$\chi_{6027}(40,\cdot)$$ 6027.cw 42 No $$-1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{42}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{6027}(43,\cdot)$$ 6027.dx 140 No $$1$$ $$1$$ $$e\left(\frac{43}{70}\right)$$ $$e\left(\frac{8}{35}\right)$$ $$e\left(\frac{31}{70}\right)$$ $$e\left(\frac{59}{70}\right)$$ $$e\left(\frac{2}{35}\right)$$ $$e\left(\frac{93}{140}\right)$$ $$e\left(\frac{121}{140}\right)$$ $$e\left(\frac{16}{35}\right)$$ $$e\left(\frac{3}{140}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{6027}(44,\cdot)$$ 6027.ee 168 Yes $$1$$ $$1$$ $$e\left(\frac{17}{84}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{41}{168}\right)$$ $$e\left(\frac{51}{56}\right)$$ $$e\left(\frac{17}{21}\right)$$ $$e\left(\frac{107}{168}\right)$$ $$e\left(\frac{1}{24}\right)$$
$$\chi_{6027}(46,\cdot)$$ 6027.et 420 No $$1$$ $$1$$ $$e\left(\frac{193}{210}\right)$$ $$e\left(\frac{88}{105}\right)$$ $$e\left(\frac{61}{210}\right)$$ $$e\left(\frac{53}{70}\right)$$ $$e\left(\frac{22}{105}\right)$$ $$e\left(\frac{253}{420}\right)$$ $$e\left(\frac{47}{140}\right)$$ $$e\left(\frac{71}{105}\right)$$ $$e\left(\frac{103}{420}\right)$$ $$e\left(\frac{17}{60}\right)$$
$$\chi_{6027}(47,\cdot)$$ 6027.ew 840 Yes $$-1$$ $$1$$ $$e\left(\frac{103}{420}\right)$$ $$e\left(\frac{103}{210}\right)$$ $$e\left(\frac{211}{420}\right)$$ $$e\left(\frac{103}{140}\right)$$ $$e\left(\frac{157}{210}\right)$$ $$e\left(\frac{283}{840}\right)$$ $$e\left(\frac{197}{280}\right)$$ $$e\left(\frac{103}{105}\right)$$ $$e\left(\frac{253}{840}\right)$$ $$e\left(\frac{47}{120}\right)$$
$$\chi_{6027}(50,\cdot)$$ 6027.m 4 No $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-i$$
$$\chi_{6027}(52,\cdot)$$ 6027.ex 840 No $$1$$ $$1$$ $$e\left(\frac{239}{420}\right)$$ $$e\left(\frac{29}{210}\right)$$ $$e\left(\frac{143}{420}\right)$$ $$e\left(\frac{99}{140}\right)$$ $$e\left(\frac{191}{210}\right)$$ $$e\left(\frac{149}{840}\right)$$ $$e\left(\frac{31}{280}\right)$$ $$e\left(\frac{29}{105}\right)$$ $$e\left(\frac{59}{840}\right)$$ $$e\left(\frac{61}{120}\right)$$
$$\chi_{6027}(53,\cdot)$$ 6027.eu 840 Yes $$1$$ $$1$$ $$e\left(\frac{101}{420}\right)$$ $$e\left(\frac{101}{210}\right)$$ $$e\left(\frac{107}{420}\right)$$ $$e\left(\frac{101}{140}\right)$$ $$e\left(\frac{52}{105}\right)$$ $$e\left(\frac{41}{840}\right)$$ $$e\left(\frac{219}{280}\right)$$ $$e\left(\frac{101}{105}\right)$$ $$e\left(\frac{611}{840}\right)$$ $$e\left(\frac{49}{120}\right)$$
$$\chi_{6027}(55,\cdot)$$ 6027.dc 56 No $$1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{33}{56}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{39}{56}\right)$$ $$e\left(\frac{1}{8}\right)$$
$$\chi_{6027}(58,\cdot)$$ 6027.ev 840 No $$-1$$ $$1$$ $$e\left(\frac{289}{420}\right)$$ $$e\left(\frac{79}{210}\right)$$ $$e\left(\frac{223}{420}\right)$$ $$e\left(\frac{9}{140}\right)$$ $$e\left(\frac{23}{105}\right)$$ $$e\left(\frac{319}{840}\right)$$ $$e\left(\frac{41}{280}\right)$$ $$e\left(\frac{79}{105}\right)$$ $$e\left(\frac{349}{840}\right)$$ $$e\left(\frac{11}{120}\right)$$