Properties

Label 7605.cn
Modulus 76057605
Conductor 585585
Order 1212
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(7605, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([2,6,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(3629,7605)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 76057605
Conductor: 585585
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 585.cn
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(ζ12)\Q(\zeta_{12})
Fixed field: 12.12.10848744628503862876453125.1

Characters in Galois orbit

Character 1-1 11 22 44 77 88 1111 1414 1616 1717 1919 2222
χ7605(3629,)\chi_{7605}(3629,\cdot) 11 11 i-i 1-1 e(112)e\left(\frac{1}{12}\right) ii i-i e(56)e\left(\frac{5}{6}\right) 11 e(16)e\left(\frac{1}{6}\right) e(512)e\left(\frac{5}{12}\right) 1-1
χ7605(4244,)\chi_{7605}(4244,\cdot) 11 11 i-i 1-1 e(512)e\left(\frac{5}{12}\right) ii i-i e(16)e\left(\frac{1}{6}\right) 11 e(56)e\left(\frac{5}{6}\right) e(112)e\left(\frac{1}{12}\right) 1-1
χ7605(5159,)\chi_{7605}(5159,\cdot) 11 11 ii 1-1 e(712)e\left(\frac{7}{12}\right) i-i ii e(56)e\left(\frac{5}{6}\right) 11 e(16)e\left(\frac{1}{6}\right) e(1112)e\left(\frac{11}{12}\right) 1-1
χ7605(7079,)\chi_{7605}(7079,\cdot) 11 11 ii 1-1 e(1112)e\left(\frac{11}{12}\right) i-i ii e(16)e\left(\frac{1}{6}\right) 11 e(56)e\left(\frac{5}{6}\right) e(712)e\left(\frac{7}{12}\right) 1-1