Properties

Label 1260.949
Modulus 12601260
Conductor 315315
Order 66
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) M = H._module chi = DirichletCharacter(H, M([0,2,3,4]))
 
Copy content pari:[g,chi] = znchar(Mod(949,1260))
 

Basic properties

Modulus: 12601260
Conductor: 315315
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 66
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ315(4,)\chi_{315}(4,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 1260.di

χ1260(709,)\chi_{1260}(709,\cdot) χ1260(949,)\chi_{1260}(949,\cdot)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: Q(ζ3)\mathbb{Q}(\zeta_3)
Fixed field: 6.6.1969120125.2

Values on generators

(631,281,757,1081)(631,281,757,1081)(1,e(13),1,e(23))(1,e\left(\frac{1}{3}\right),-1,e\left(\frac{2}{3}\right))

First values

aa 1-1111111131317171919232329293131373741414343
χ1260(949,a) \chi_{ 1260 }(949, a) 111111e(16)e\left(\frac{1}{6}\right)e(16)e\left(\frac{1}{6}\right)e(13)e\left(\frac{1}{3}\right)1-1e(13)e\left(\frac{1}{3}\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)e(56)e\left(\frac{5}{6}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ1260(949,a)   \chi_{ 1260 }(949,a) \; at   a=\;a = e.g. 2