Properties

Label 2898.2351
Modulus 28982898
Conductor 14491449
Order 6666
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(2898, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([11,33,3]))
 
Copy content pari:[g,chi] = znchar(Mod(2351,2898))
 

Basic properties

Modulus: 28982898
Conductor: 14491449
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 6666
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ1449(902,)\chi_{1449}(902,\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 2898.cl

χ2898(83,)\chi_{2898}(83,\cdot) χ2898(293,)\chi_{2898}(293,\cdot) χ2898(419,)\chi_{2898}(419,\cdot) χ2898(797,)\chi_{2898}(797,\cdot) χ2898(839,)\chi_{2898}(839,\cdot) χ2898(1049,)\chi_{2898}(1049,\cdot) χ2898(1091,)\chi_{2898}(1091,\cdot) χ2898(1217,)\chi_{2898}(1217,\cdot) χ2898(1469,)\chi_{2898}(1469,\cdot) χ2898(1721,)\chi_{2898}(1721,\cdot) χ2898(1805,)\chi_{2898}(1805,\cdot) χ2898(1847,)\chi_{2898}(1847,\cdot) χ2898(2057,)\chi_{2898}(2057,\cdot) χ2898(2183,)\chi_{2898}(2183,\cdot) χ2898(2225,)\chi_{2898}(2225,\cdot) χ2898(2351,)\chi_{2898}(2351,\cdot) χ2898(2435,)\chi_{2898}(2435,\cdot) χ2898(2687,)\chi_{2898}(2687,\cdot) χ2898(2729,)\chi_{2898}(2729,\cdot) χ2898(2813,)\chi_{2898}(2813,\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(ζ33)\Q(\zeta_{33})
Fixed field: Number field defined by a degree 66 polynomial

Values on generators

(1289,829,1891)(1289,829,1891)(e(16),1,e(122))(e\left(\frac{1}{6}\right),-1,e\left(\frac{1}{22}\right))

First values

aa 1-11155111113131717191925252929313137374141
χ2898(2351,a) \chi_{ 2898 }(2351, a) 1-111e(2566)e\left(\frac{25}{66}\right)e(1933)e\left(\frac{19}{33}\right)e(3166)e\left(\frac{31}{66}\right)e(722)e\left(\frac{7}{22}\right)e(211)e\left(\frac{2}{11}\right)e(2533)e\left(\frac{25}{33}\right)e(6566)e\left(\frac{65}{66}\right)e(766)e\left(\frac{7}{66}\right)e(2122)e\left(\frac{21}{22}\right)e(2933)e\left(\frac{29}{33}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2898(2351,a)   \chi_{ 2898 }(2351,a) \; at   a=\;a = e.g. 2