Properties

Label 2898.89
Modulus 28982898
Conductor 483483
Order 6666
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(2898, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([33,55,15]))
 
Copy content pari:[g,chi] = znchar(Mod(89,2898))
 

Basic properties

Modulus: 28982898
Conductor: 483483
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 χ483(89,)\chi_{483}(89,\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.co

χ2898(17,)\chi_{2898}(17,\cdot) χ2898(89,)\chi_{2898}(89,\cdot) χ2898(143,)\chi_{2898}(143,\cdot) χ2898(341,)\chi_{2898}(341,\cdot) χ2898(467,)\chi_{2898}(467,\cdot) χ2898(521,)\chi_{2898}(521,\cdot) χ2898(773,)\chi_{2898}(773,\cdot) χ2898(845,)\chi_{2898}(845,\cdot) χ2898(971,)\chi_{2898}(971,\cdot) χ2898(1349,)\chi_{2898}(1349,\cdot) χ2898(1529,)\chi_{2898}(1529,\cdot) χ2898(1601,)\chi_{2898}(1601,\cdot) χ2898(1781,)\chi_{2898}(1781,\cdot) χ2898(1907,)\chi_{2898}(1907,\cdot) χ2898(2159,)\chi_{2898}(2159,\cdot) χ2898(2357,)\chi_{2898}(2357,\cdot) χ2898(2411,)\chi_{2898}(2411,\cdot) χ2898(2537,)\chi_{2898}(2537,\cdot) χ2898(2609,)\chi_{2898}(2609,\cdot) χ2898(2735,)\chi_{2898}(2735,\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)(1,e(56),e(522))(-1,e\left(\frac{5}{6}\right),e\left(\frac{5}{22}\right))

First values

aa 1-11155111113131717191925252929313137374141
χ2898(89,a) \chi_{ 2898 }(89, a) 1-111e(5966)e\left(\frac{59}{66}\right)e(2933)e\left(\frac{29}{33}\right)e(1522)e\left(\frac{15}{22}\right)e(6166)e\left(\frac{61}{66}\right)e(1933)e\left(\frac{19}{33}\right)e(2633)e\left(\frac{26}{33}\right)e(1322)e\left(\frac{13}{22}\right)e(1366)e\left(\frac{13}{66}\right)e(2966)e\left(\frac{29}{66}\right)e(811)e\left(\frac{8}{11}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2898(89,a)   \chi_{ 2898 }(89,a) \; at   a=\;a = e.g. 2