Properties

Label 1480.137
Modulus 14801480
Conductor 185185
Order 1212
Real no
Primitive no
Minimal yes
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1480, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([0,0,3,4]))
 
Copy content pari:[g,chi] = znchar(Mod(137,1480))
 

Basic properties

Modulus: 14801480
Conductor: 185185
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 χ185(137,)\chi_{185}(137,\cdot)
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)
 

Galois orbit 1480.cv

χ1480(137,)\chi_{1480}(137,\cdot) χ1480(417,)\chi_{1480}(417,\cdot) χ1480(433,)\chi_{1480}(433,\cdot) χ1480(713,)\chi_{1480}(713,\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(ζ12)\Q(\zeta_{12})
Fixed field: 12.0.6860311433439453125.1

Values on generators

(1111,741,297,1001)(1111,741,297,1001)(1,1,i,e(13))(1,1,i,e\left(\frac{1}{3}\right))

First values

aa 1-1113377991111131317171919212123232727
χ1480(137,a) \chi_{ 1480 }(137, a) 1-111e(512)e\left(\frac{5}{12}\right)e(1112)e\left(\frac{11}{12}\right)e(56)e\left(\frac{5}{6}\right)11e(512)e\left(\frac{5}{12}\right)e(712)e\left(\frac{7}{12}\right)e(16)e\left(\frac{1}{6}\right)e(13)e\left(\frac{1}{3}\right)i-iii
Copy content sage:chi.jacobi_sum(n)
 
χ1480(137,a)   \chi_{ 1480 }(137,a) \; at   a=\;a = e.g. 2