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Properties

Label 592.ch
Modulus 592592
Conductor 296296
Order 3636
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(592, base_ring=CyclotomicField(36)) M = H._module chi = DirichletCharacter(H, M([18,18,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(39,592)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 592592
Conductor: 296296
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 3636
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 296.bj
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ36)\Q(\zeta_{36})
Fixed field: 36.36.138892919952333446776057851184385905517238171566853781889085447929331712.1

Characters in Galois orbit

Character −1-1 11 33 55 77 99 1111 1313 1515 1717 1919 2121
χ592(39,⋅)\chi_{592}(39,\cdot) 11 11 e(1318)e\left(\frac{13}{18}\right) e(536)e\left(\frac{5}{36}\right) e(718)e\left(\frac{7}{18}\right) e(49)e\left(\frac{4}{9}\right) e(56)e\left(\frac{5}{6}\right) e(2936)e\left(\frac{29}{36}\right) e(3136)e\left(\frac{31}{36}\right) e(736)e\left(\frac{7}{36}\right) e(3536)e\left(\frac{35}{36}\right) e(19)e\left(\frac{1}{9}\right)
χ592(55,⋅)\chi_{592}(55,\cdot) 11 11 e(518)e\left(\frac{5}{18}\right) e(1336)e\left(\frac{13}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(16)e\left(\frac{1}{6}\right) e(2536)e\left(\frac{25}{36}\right) e(2336)e\left(\frac{23}{36}\right) e(1136)e\left(\frac{11}{36}\right) e(1936)e\left(\frac{19}{36}\right) e(89)e\left(\frac{8}{9}\right)
χ592(87,⋅)\chi_{592}(87,\cdot) 11 11 e(1718)e\left(\frac{17}{18}\right) e(1936)e\left(\frac{19}{36}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(16)e\left(\frac{1}{6}\right) e(3136)e\left(\frac{31}{36}\right) e(1736)e\left(\frac{17}{36}\right) e(536)e\left(\frac{5}{36}\right) e(2536)e\left(\frac{25}{36}\right) e(29)e\left(\frac{2}{9}\right)
χ592(135,⋅)\chi_{592}(135,\cdot) 11 11 e(1718)e\left(\frac{17}{18}\right) e(136)e\left(\frac{1}{36}\right) e(518)e\left(\frac{5}{18}\right) e(89)e\left(\frac{8}{9}\right) e(16)e\left(\frac{1}{6}\right) e(1336)e\left(\frac{13}{36}\right) e(3536)e\left(\frac{35}{36}\right) e(2336)e\left(\frac{23}{36}\right) e(736)e\left(\frac{7}{36}\right) e(29)e\left(\frac{2}{9}\right)
χ592(167,⋅)\chi_{592}(167,\cdot) 11 11 e(518)e\left(\frac{5}{18}\right) e(3136)e\left(\frac{31}{36}\right) e(1118)e\left(\frac{11}{18}\right) e(59)e\left(\frac{5}{9}\right) e(16)e\left(\frac{1}{6}\right) e(736)e\left(\frac{7}{36}\right) e(536)e\left(\frac{5}{36}\right) e(2936)e\left(\frac{29}{36}\right) e(136)e\left(\frac{1}{36}\right) e(89)e\left(\frac{8}{9}\right)
χ592(183,⋅)\chi_{592}(183,\cdot) 11 11 e(1318)e\left(\frac{13}{18}\right) e(2336)e\left(\frac{23}{36}\right) e(718)e\left(\frac{7}{18}\right) e(49)e\left(\frac{4}{9}\right) e(56)e\left(\frac{5}{6}\right) e(1136)e\left(\frac{11}{36}\right) e(1336)e\left(\frac{13}{36}\right) e(2536)e\left(\frac{25}{36}\right) e(1736)e\left(\frac{17}{36}\right) e(19)e\left(\frac{1}{9}\right)
χ592(279,⋅)\chi_{592}(279,\cdot) 11 11 e(118)e\left(\frac{1}{18}\right) e(1736)e\left(\frac{17}{36}\right) e(1318)e\left(\frac{13}{18}\right) e(19)e\left(\frac{1}{9}\right) e(56)e\left(\frac{5}{6}\right) e(536)e\left(\frac{5}{36}\right) e(1936)e\left(\frac{19}{36}\right) e(3136)e\left(\frac{31}{36}\right) e(1136)e\left(\frac{11}{36}\right) e(79)e\left(\frac{7}{9}\right)
χ592(311,⋅)\chi_{592}(311,\cdot) 11 11 e(718)e\left(\frac{7}{18}\right) e(2936)e\left(\frac{29}{36}\right) e(118)e\left(\frac{1}{18}\right) e(79)e\left(\frac{7}{9}\right) e(56)e\left(\frac{5}{6}\right) e(1736)e\left(\frac{17}{36}\right) e(736)e\left(\frac{7}{36}\right) e(1936)e\left(\frac{19}{36}\right) e(2336)e\left(\frac{23}{36}\right) e(49)e\left(\frac{4}{9}\right)
χ592(375,⋅)\chi_{592}(375,\cdot) 11 11 e(1118)e\left(\frac{11}{18}\right) e(736)e\left(\frac{7}{36}\right) e(1718)e\left(\frac{17}{18}\right) e(29)e\left(\frac{2}{9}\right) e(16)e\left(\frac{1}{6}\right) e(1936)e\left(\frac{19}{36}\right) e(2936)e\left(\frac{29}{36}\right) e(1736)e\left(\frac{17}{36}\right) e(1336)e\left(\frac{13}{36}\right) e(59)e\left(\frac{5}{9}\right)
χ592(439,⋅)\chi_{592}(439,\cdot) 11 11 e(1118)e\left(\frac{11}{18}\right) e(2536)e\left(\frac{25}{36}\right) e(1718)e\left(\frac{17}{18}\right) e(29)e\left(\frac{2}{9}\right) e(16)e\left(\frac{1}{6}\right) e(136)e\left(\frac{1}{36}\right) e(1136)e\left(\frac{11}{36}\right) e(3536)e\left(\frac{35}{36}\right) e(3136)e\left(\frac{31}{36}\right) e(59)e\left(\frac{5}{9}\right)
χ592(503,⋅)\chi_{592}(503,\cdot) 11 11 e(718)e\left(\frac{7}{18}\right) e(1136)e\left(\frac{11}{36}\right) e(118)e\left(\frac{1}{18}\right) e(79)e\left(\frac{7}{9}\right) e(56)e\left(\frac{5}{6}\right) e(3536)e\left(\frac{35}{36}\right) e(2536)e\left(\frac{25}{36}\right) e(136)e\left(\frac{1}{36}\right) e(536)e\left(\frac{5}{36}\right) e(49)e\left(\frac{4}{9}\right)
χ592(535,⋅)\chi_{592}(535,\cdot) 11 11 e(118)e\left(\frac{1}{18}\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(56)e\left(\frac{5}{6}\right) e(2336)e\left(\frac{23}{36}\right) e(136)e\left(\frac{1}{36}\right) e(1336)e\left(\frac{13}{36}\right) e(2936)e\left(\frac{29}{36}\right) e(79)e\left(\frac{7}{9}\right)