↑

Properties

Modulus 405405
Structure C2×C108C_{2}\times C_{108}
Order 216216

Learn more

Show commands: PariGP / SageMath

sage: H = DirichletGroup(405)
 
pari: g = idealstar(,405,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 216
sage: H.invariants()
 
pari: g.cyc
 
Structure = C2×C108C_{2}\times C_{108}
sage: H.gens()
 
pari: g.gen
 
Generators = χ405(326,⋅)\chi_{405}(326,\cdot), χ405(82,⋅)\chi_{405}(82,\cdot)

First 32 of 216 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 11 22 44 77 88 1111 1313 1414 1616 1717 1919
χ405(1,⋅)\chi_{405}(1,\cdot) 405.a 1 no 11 11 11 11 11 11 11 11 11 11 11 11
χ405(2,⋅)\chi_{405}(2,\cdot) 405.x 108 yes 11 11 e(29108)e\left(\frac{29}{108}\right) e(2954)e\left(\frac{29}{54}\right) e(59108)e\left(\frac{59}{108}\right) e(2936)e\left(\frac{29}{36}\right) e(1354)e\left(\frac{13}{54}\right) e(97108)e\left(\frac{97}{108}\right) e(2227)e\left(\frac{22}{27}\right) e(227)e\left(\frac{2}{27}\right) e(3136)e\left(\frac{31}{36}\right) e(718)e\left(\frac{7}{18}\right)
χ405(4,⋅)\chi_{405}(4,\cdot) 405.t 54 yes 11 11 e(2954)e\left(\frac{29}{54}\right) e(227)e\left(\frac{2}{27}\right) e(554)e\left(\frac{5}{54}\right) e(1118)e\left(\frac{11}{18}\right) e(1327)e\left(\frac{13}{27}\right) e(4354)e\left(\frac{43}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(427)e\left(\frac{4}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(79)e\left(\frac{7}{9}\right)
χ405(7,⋅)\chi_{405}(7,\cdot) 405.w 108 yes −1-1 11 e(59108)e\left(\frac{59}{108}\right) e(554)e\left(\frac{5}{54}\right) e(107108)e\left(\frac{107}{108}\right) e(2336)e\left(\frac{23}{36}\right) e(2327)e\left(\frac{23}{27}\right) e(13108)e\left(\frac{13}{108}\right) e(2954)e\left(\frac{29}{54}\right) e(527)e\left(\frac{5}{27}\right) e(136)e\left(\frac{1}{36}\right) e(1318)e\left(\frac{13}{18}\right)
χ405(8,⋅)\chi_{405}(8,\cdot) 405.r 36 no 11 11 e(2936)e\left(\frac{29}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(2336)e\left(\frac{23}{36}\right) e(512)e\left(\frac{5}{12}\right) e(1318)e\left(\frac{13}{18}\right) e(2536)e\left(\frac{25}{36}\right) e(49)e\left(\frac{4}{9}\right) e(29)e\left(\frac{2}{9}\right) e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right)
χ405(11,⋅)\chi_{405}(11,\cdot) 405.u 54 no −1-1 11 e(1354)e\left(\frac{13}{54}\right) e(1327)e\left(\frac{13}{27}\right) e(2327)e\left(\frac{23}{27}\right) e(1318)e\left(\frac{13}{18}\right) e(754)e\left(\frac{7}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(554)e\left(\frac{5}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(59)e\left(\frac{5}{9}\right)
χ405(13,⋅)\chi_{405}(13,\cdot) 405.w 108 yes −1-1 11 e(97108)e\left(\frac{97}{108}\right) e(4354)e\left(\frac{43}{54}\right) e(13108)e\left(\frac{13}{108}\right) e(2536)e\left(\frac{25}{36}\right) e(2527)e\left(\frac{25}{27}\right) e(47108)e\left(\frac{47}{108}\right) e(154)e\left(\frac{1}{54}\right) e(1627)e\left(\frac{16}{27}\right) e(2336)e\left(\frac{23}{36}\right) e(1118)e\left(\frac{11}{18}\right)
χ405(14,⋅)\chi_{405}(14,\cdot) 405.v 54 yes −1-1 11 e(2227)e\left(\frac{22}{27}\right) e(1727)e\left(\frac{17}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(49)e\left(\frac{4}{9}\right) e(554)e\left(\frac{5}{54}\right) e(154)e\left(\frac{1}{54}\right) e(1954)e\left(\frac{19}{54}\right) e(727)e\left(\frac{7}{27}\right) e(89)e\left(\frac{8}{9}\right) e(19)e\left(\frac{1}{9}\right)
χ405(16,⋅)\chi_{405}(16,\cdot) 405.q 27 no 11 11 e(227)e\left(\frac{2}{27}\right) e(427)e\left(\frac{4}{27}\right) e(527)e\left(\frac{5}{27}\right) e(29)e\left(\frac{2}{9}\right) e(2627)e\left(\frac{26}{27}\right) e(1627)e\left(\frac{16}{27}\right) e(727)e\left(\frac{7}{27}\right) e(827)e\left(\frac{8}{27}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right)
χ405(17,⋅)\chi_{405}(17,\cdot) 405.r 36 no 11 11 e(3136)e\left(\frac{31}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(136)e\left(\frac{1}{36}\right) e(712)e\left(\frac{7}{12}\right) e(1718)e\left(\frac{17}{18}\right) e(2336)e\left(\frac{23}{36}\right) e(89)e\left(\frac{8}{9}\right) e(49)e\left(\frac{4}{9}\right) e(512)e\left(\frac{5}{12}\right) e(56)e\left(\frac{5}{6}\right)
χ405(19,⋅)\chi_{405}(19,\cdot) 405.p 18 no 11 11 e(718)e\left(\frac{7}{18}\right) e(79)e\left(\frac{7}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(16)e\left(\frac{1}{6}\right) e(59)e\left(\frac{5}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(19)e\left(\frac{1}{9}\right) e(59)e\left(\frac{5}{9}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right)
χ405(22,⋅)\chi_{405}(22,\cdot) 405.w 108 yes −1-1 11 e(55108)e\left(\frac{55}{108}\right) e(154)e\left(\frac{1}{54}\right) e(43108)e\left(\frac{43}{108}\right) e(1936)e\left(\frac{19}{36}\right) e(1027)e\left(\frac{10}{27}\right) e(89108)e\left(\frac{89}{108}\right) e(4954)e\left(\frac{49}{54}\right) e(127)e\left(\frac{1}{27}\right) e(2936)e\left(\frac{29}{36}\right) e(1718)e\left(\frac{17}{18}\right)
χ405(23,⋅)\chi_{405}(23,\cdot) 405.x 108 yes 11 11 e(103108)e\left(\frac{103}{108}\right) e(4954)e\left(\frac{49}{54}\right) e(1108)e\left(\frac{1}{108}\right) e(3136)e\left(\frac{31}{36}\right) e(3554)e\left(\frac{35}{54}\right) e(95108)e\left(\frac{95}{108}\right) e(2627)e\left(\frac{26}{27}\right) e(2227)e\left(\frac{22}{27}\right) e(1736)e\left(\frac{17}{36}\right) e(518)e\left(\frac{5}{18}\right)
χ405(26,⋅)\chi_{405}(26,\cdot) 405.i 6 no −1-1 11 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right) −1-1 11
χ405(28,⋅)\chi_{405}(28,\cdot) 405.l 12 no −1-1 11 e(112)e\left(\frac{1}{12}\right) e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) ii e(13)e\left(\frac{1}{3}\right) e(1112)e\left(\frac{11}{12}\right) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) −i-i −1-1
χ405(29,⋅)\chi_{405}(29,\cdot) 405.v 54 yes −1-1 11 e(527)e\left(\frac{5}{27}\right) e(1027)e\left(\frac{10}{27}\right) e(2554)e\left(\frac{25}{54}\right) e(59)e\left(\frac{5}{9}\right) e(4954)e\left(\frac{49}{54}\right) e(5354)e\left(\frac{53}{54}\right) e(3554)e\left(\frac{35}{54}\right) e(2027)e\left(\frac{20}{27}\right) e(19)e\left(\frac{1}{9}\right) e(89)e\left(\frac{8}{9}\right)
χ405(31,⋅)\chi_{405}(31,\cdot) 405.q 27 no 11 11 e(1027)e\left(\frac{10}{27}\right) e(2027)e\left(\frac{20}{27}\right) e(2527)e\left(\frac{25}{27}\right) e(19)e\left(\frac{1}{9}\right) e(2227)e\left(\frac{22}{27}\right) e(2627)e\left(\frac{26}{27}\right) e(827)e\left(\frac{8}{27}\right) e(1327)e\left(\frac{13}{27}\right) e(29)e\left(\frac{2}{9}\right) e(79)e\left(\frac{7}{9}\right)
χ405(32,⋅)\chi_{405}(32,\cdot) 405.x 108 yes 11 11 e(37108)e\left(\frac{37}{108}\right) e(3754)e\left(\frac{37}{54}\right) e(79108)e\left(\frac{79}{108}\right) e(136)e\left(\frac{1}{36}\right) e(1154)e\left(\frac{11}{54}\right) e(53108)e\left(\frac{53}{108}\right) e(227)e\left(\frac{2}{27}\right) e(1027)e\left(\frac{10}{27}\right) e(1136)e\left(\frac{11}{36}\right) e(1718)e\left(\frac{17}{18}\right)
χ405(34,⋅)\chi_{405}(34,\cdot) 405.t 54 yes 11 11 e(754)e\left(\frac{7}{54}\right) e(727)e\left(\frac{7}{27}\right) e(3154)e\left(\frac{31}{54}\right) e(718)e\left(\frac{7}{18}\right) e(527)e\left(\frac{5}{27}\right) e(2954)e\left(\frac{29}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(518)e\left(\frac{5}{18}\right) e(29)e\left(\frac{2}{9}\right)
χ405(37,⋅)\chi_{405}(37,\cdot) 405.s 36 no −1-1 11 e(136)e\left(\frac{1}{36}\right) e(118)e\left(\frac{1}{18}\right) e(2536)e\left(\frac{25}{36}\right) e(112)e\left(\frac{1}{12}\right) e(19)e\left(\frac{1}{9}\right) e(3536)e\left(\frac{35}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(1112)e\left(\frac{11}{12}\right) e(56)e\left(\frac{5}{6}\right)
χ405(38,⋅)\chi_{405}(38,\cdot) 405.x 108 yes 11 11 e(71108)e\left(\frac{71}{108}\right) e(1754)e\left(\frac{17}{54}\right) e(29108)e\left(\frac{29}{108}\right) e(3536)e\left(\frac{35}{36}\right) e(4354)e\left(\frac{43}{54}\right) e(55108)e\left(\frac{55}{108}\right) e(2527)e\left(\frac{25}{27}\right) e(1727)e\left(\frac{17}{27}\right) e(2536)e\left(\frac{25}{36}\right) e(118)e\left(\frac{1}{18}\right)
χ405(41,⋅)\chi_{405}(41,\cdot) 405.u 54 no −1-1 11 e(5354)e\left(\frac{53}{54}\right) e(2627)e\left(\frac{26}{27}\right) e(1927)e\left(\frac{19}{27}\right) e(1718)e\left(\frac{17}{18}\right) e(4154)e\left(\frac{41}{54}\right) e(2327)e\left(\frac{23}{27}\right) e(3754)e\left(\frac{37}{54}\right) e(2527)e\left(\frac{25}{27}\right) e(718)e\left(\frac{7}{18}\right) e(19)e\left(\frac{1}{9}\right)
χ405(43,⋅)\chi_{405}(43,\cdot) 405.w 108 yes −1-1 11 e(17108)e\left(\frac{17}{108}\right) e(1754)e\left(\frac{17}{54}\right) e(29108)e\left(\frac{29}{108}\right) e(1736)e\left(\frac{17}{36}\right) e(827)e\left(\frac{8}{27}\right) e(55108)e\left(\frac{55}{108}\right) e(2354)e\left(\frac{23}{54}\right) e(1727)e\left(\frac{17}{27}\right) e(736)e\left(\frac{7}{36}\right) e(118)e\left(\frac{1}{18}\right)
χ405(44,⋅)\chi_{405}(44,\cdot) 405.n 18 no −1-1 11 e(79)e\left(\frac{7}{9}\right) e(59)e\left(\frac{5}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(13)e\left(\frac{1}{3}\right) e(1118)e\left(\frac{11}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right)
χ405(46,⋅)\chi_{405}(46,\cdot) 405.k 9 no 11 11 e(29)e\left(\frac{2}{9}\right) e(49)e\left(\frac{4}{9}\right) e(59)e\left(\frac{5}{9}\right) e(23)e\left(\frac{2}{3}\right) e(89)e\left(\frac{8}{9}\right) e(79)e\left(\frac{7}{9}\right) e(79)e\left(\frac{7}{9}\right) e(89)e\left(\frac{8}{9}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right)
χ405(47,⋅)\chi_{405}(47,\cdot) 405.x 108 yes 11 11 e(41108)e\left(\frac{41}{108}\right) e(4154)e\left(\frac{41}{54}\right) e(35108)e\left(\frac{35}{108}\right) e(536)e\left(\frac{5}{36}\right) e(3754)e\left(\frac{37}{54}\right) e(85108)e\left(\frac{85}{108}\right) e(1927)e\left(\frac{19}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(1936)e\left(\frac{19}{36}\right) e(1318)e\left(\frac{13}{18}\right)
χ405(49,⋅)\chi_{405}(49,\cdot) 405.t 54 yes 11 11 e(554)e\left(\frac{5}{54}\right) e(527)e\left(\frac{5}{27}\right) e(5354)e\left(\frac{53}{54}\right) e(518)e\left(\frac{5}{18}\right) e(1927)e\left(\frac{19}{27}\right) e(1354)e\left(\frac{13}{54}\right) e(227)e\left(\frac{2}{27}\right) e(1027)e\left(\frac{10}{27}\right) e(118)e\left(\frac{1}{18}\right) e(49)e\left(\frac{4}{9}\right)
χ405(52,⋅)\chi_{405}(52,\cdot) 405.w 108 yes −1-1 11 e(47108)e\left(\frac{47}{108}\right) e(4754)e\left(\frac{47}{54}\right) e(23108)e\left(\frac{23}{108}\right) e(1136)e\left(\frac{11}{36}\right) e(1127)e\left(\frac{11}{27}\right) e(25108)e\left(\frac{25}{108}\right) e(3554)e\left(\frac{35}{54}\right) e(2027)e\left(\frac{20}{27}\right) e(1336)e\left(\frac{13}{36}\right) e(718)e\left(\frac{7}{18}\right)
χ405(53,⋅)\chi_{405}(53,\cdot) 405.m 12 no 11 11 e(712)e\left(\frac{7}{12}\right) e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) −i-i e(56)e\left(\frac{5}{6}\right) e(1112)e\left(\frac{11}{12}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) ii −1-1
χ405(56,⋅)\chi_{405}(56,\cdot) 405.u 54 no −1-1 11 e(1954)e\left(\frac{19}{54}\right) e(1927)e\left(\frac{19}{27}\right) e(1727)e\left(\frac{17}{27}\right) e(118)e\left(\frac{1}{18}\right) e(3154)e\left(\frac{31}{54}\right) e(2227)e\left(\frac{22}{27}\right) e(5354)e\left(\frac{53}{54}\right) e(1127)e\left(\frac{11}{27}\right) e(1118)e\left(\frac{11}{18}\right) e(89)e\left(\frac{8}{9}\right)
χ405(58,⋅)\chi_{405}(58,\cdot) 405.w 108 yes −1-1 11 e(49108)e\left(\frac{49}{108}\right) e(4954)e\left(\frac{49}{54}\right) e(1108)e\left(\frac{1}{108}\right) e(1336)e\left(\frac{13}{36}\right) e(427)e\left(\frac{4}{27}\right) e(95108)e\left(\frac{95}{108}\right) e(2554)e\left(\frac{25}{54}\right) e(2227)e\left(\frac{22}{27}\right) e(3536)e\left(\frac{35}{36}\right) e(518)e\left(\frac{5}{18}\right)
χ405(59,⋅)\chi_{405}(59,\cdot) 405.v 54 yes −1-1 11 e(727)e\left(\frac{7}{27}\right) e(1427)e\left(\frac{14}{27}\right) e(3554)e\left(\frac{35}{54}\right) e(79)e\left(\frac{7}{9}\right) e(4754)e\left(\frac{47}{54}\right) e(3154)e\left(\frac{31}{54}\right) e(4954)e\left(\frac{49}{54}\right) e(127)e\left(\frac{1}{27}\right) e(59)e\left(\frac{5}{9}\right) e(49)e\left(\frac{4}{9}\right)
Click here to search among the remaining 184 characters.