Properties

Label 1800.ck
Modulus 18001800
Conductor 360360
Order 1212
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1800, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([0,6,4,3])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(157,1800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 18001800
Conductor: 360360
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 1212
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 360.bu
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ12)\Q(\zeta_{12})
Fixed field: 12.0.22039921152000000000.1

Characters in Galois orbit

Character 1-1 11 77 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ1800(157,)\chi_{1800}(157,\cdot) 1-1 11 e(712)e\left(\frac{7}{12}\right) e(56)e\left(\frac{5}{6}\right) e(1112)e\left(\frac{11}{12}\right) ii 11 e(512)e\left(\frac{5}{12}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) i-i e(23)e\left(\frac{2}{3}\right)
χ1800(493,)\chi_{1800}(493,\cdot) 1-1 11 e(512)e\left(\frac{5}{12}\right) e(16)e\left(\frac{1}{6}\right) e(112)e\left(\frac{1}{12}\right) i-i 11 e(712)e\left(\frac{7}{12}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) ii e(13)e\left(\frac{1}{3}\right)
χ1800(1093,)\chi_{1800}(1093,\cdot) 1-1 11 e(112)e\left(\frac{1}{12}\right) e(56)e\left(\frac{5}{6}\right) e(512)e\left(\frac{5}{12}\right) i-i 11 e(1112)e\left(\frac{11}{12}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) ii e(23)e\left(\frac{2}{3}\right)
χ1800(1357,)\chi_{1800}(1357,\cdot) 1-1 11 e(1112)e\left(\frac{11}{12}\right) e(16)e\left(\frac{1}{6}\right) e(712)e\left(\frac{7}{12}\right) ii 11 e(112)e\left(\frac{1}{12}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) i-i e(13)e\left(\frac{1}{3}\right)