Properties

 Modulus $1035$ Structure $$C_{132}\times C_{2}\times C_{2}$$ Order $528$

Show commands for: Pari/GP / SageMath

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

sage: H = DirichletGroup_conrey(1035)

pari: g = idealstar(,1035,2)

Character group

 sage: G.order()  pari: g.no Order = 528 sage: H.invariants()  pari: g.cyc Structure = $$C_{132}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1035}(833,\cdot)$, $\chi_{1035}(944,\cdot)$, $\chi_{1035}(919,\cdot)$

First 32 of 528 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$7$$ $$8$$ $$11$$ $$13$$ $$14$$ $$16$$ $$17$$ $$19$$
$$\chi_{1035}(1,\cdot)$$ 1035.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1035}(2,\cdot)$$ 1035.bt 132 yes $$1$$ $$1$$ $$e\left(\frac{79}{132}\right)$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{1035}(4,\cdot)$$ 1035.bl 66 yes $$1$$ $$1$$ $$e\left(\frac{13}{66}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{1035}(7,\cdot)$$ 1035.bs 132 yes $$1$$ $$1$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{43}{132}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{1035}(8,\cdot)$$ 1035.bk 44 no $$1$$ $$1$$ $$e\left(\frac{35}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{1035}(11,\cdot)$$ 1035.bm 66 no $$1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1035}(13,\cdot)$$ 1035.bv 132 yes $$-1$$ $$1$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{23}{132}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{2}{33}\right)$$ $$e\left(\frac{109}{132}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{1035}(14,\cdot)$$ 1035.br 66 yes $$1$$ $$1$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{1035}(16,\cdot)$$ 1035.bg 33 no $$1$$ $$1$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{1035}(17,\cdot)$$ 1035.bh 44 no $$-1$$ $$1$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{1035}(19,\cdot)$$ 1035.bd 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{1035}(22,\cdot)$$ 1035.y 12 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$1$$
$$\chi_{1035}(26,\cdot)$$ 1035.bc 22 no $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{1035}(28,\cdot)$$ 1035.bj 44 no $$1$$ $$1$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{23}{44}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{39}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{44}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{1035}(29,\cdot)$$ 1035.bp 66 yes $$-1$$ $$1$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{1035}(31,\cdot)$$ 1035.bg 33 no $$1$$ $$1$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{26}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{1035}(32,\cdot)$$ 1035.bt 132 yes $$1$$ $$1$$ $$e\left(\frac{131}{132}\right)$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{29}{132}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{103}{132}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{1035}(34,\cdot)$$ 1035.bn 66 yes $$-1$$ $$1$$ $$e\left(\frac{65}{66}\right)$$ $$e\left(\frac{32}{33}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1035}(37,\cdot)$$ 1035.bj 44 no $$1$$ $$1$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{1035}(38,\cdot)$$ 1035.bu 132 yes $$-1$$ $$1$$ $$e\left(\frac{61}{132}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{13}{132}\right)$$ $$e\left(\frac{17}{44}\right)$$ $$e\left(\frac{4}{33}\right)$$ $$e\left(\frac{53}{132}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{1035}(41,\cdot)$$ 1035.bo 66 no $$-1$$ $$1$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{10}{33}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{1035}(43,\cdot)$$ 1035.bs 132 yes $$1$$ $$1$$ $$e\left(\frac{115}{132}\right)$$ $$e\left(\frac{49}{66}\right)$$ $$e\left(\frac{97}{132}\right)$$ $$e\left(\frac{27}{44}\right)$$ $$e\left(\frac{47}{66}\right)$$ $$e\left(\frac{101}{132}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{16}{33}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{1035}(44,\cdot)$$ 1035.z 22 no $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{1035}(47,\cdot)$$ 1035.x 12 no $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$i$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$-1$$
$$\chi_{1035}(49,\cdot)$$ 1035.bl 66 yes $$1$$ $$1$$ $$e\left(\frac{19}{66}\right)$$ $$e\left(\frac{19}{33}\right)$$ $$e\left(\frac{43}{66}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{31}{33}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{1035}(52,\cdot)$$ 1035.bv 132 yes $$-1$$ $$1$$ $$e\left(\frac{73}{132}\right)$$ $$e\left(\frac{7}{66}\right)$$ $$e\left(\frac{61}{132}\right)$$ $$e\left(\frac{29}{44}\right)$$ $$e\left(\frac{1}{33}\right)$$ $$e\left(\frac{71}{132}\right)$$ $$e\left(\frac{1}{66}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{1035}(53,\cdot)$$ 1035.bh 44 no $$-1$$ $$1$$ $$e\left(\frac{43}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{41}{44}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{1035}(56,\cdot)$$ 1035.bm 66 no $$1$$ $$1$$ $$e\left(\frac{29}{66}\right)$$ $$e\left(\frac{29}{33}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{13}{33}\right)$$ $$e\left(\frac{8}{33}\right)$$ $$e\left(\frac{23}{33}\right)$$ $$e\left(\frac{25}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{1035}(58,\cdot)$$ 1035.bv 132 yes $$-1$$ $$1$$ $$e\left(\frac{119}{132}\right)$$ $$e\left(\frac{53}{66}\right)$$ $$e\left(\frac{47}{132}\right)$$ $$e\left(\frac{31}{44}\right)$$ $$e\left(\frac{17}{33}\right)$$ $$e\left(\frac{85}{132}\right)$$ $$e\left(\frac{17}{66}\right)$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{5}{44}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{1035}(59,\cdot)$$ 1035.bp 66 yes $$-1$$ $$1$$ $$e\left(\frac{20}{33}\right)$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{61}{66}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{5}{66}\right)$$ $$e\left(\frac{35}{66}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{1035}(61,\cdot)$$ 1035.bq 66 no $$-1$$ $$1$$ $$e\left(\frac{7}{33}\right)$$ $$e\left(\frac{14}{33}\right)$$ $$e\left(\frac{23}{66}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{41}{66}\right)$$ $$e\left(\frac{5}{33}\right)$$ $$e\left(\frac{37}{66}\right)$$ $$e\left(\frac{28}{33}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{1035}(62,\cdot)$$ 1035.bk 44 no $$1$$ $$1$$ $$e\left(\frac{21}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{7}{44}\right)$$ $$e\left(\frac{19}{44}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{37}{44}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{44}\right)$$ $$e\left(\frac{21}{22}\right)$$