Properties

Label 2898.1903
Modulus 28982898
Conductor 14491449
Order 6666
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(2898, base_ring=CyclotomicField(66)) M = H._module chi = DirichletCharacter(H, M([22,33,21]))
 
Copy content pari:[g,chi] = znchar(Mod(1903,2898))
 

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(454,)\chi_{1449}(454,\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 2898.cp

χ2898(97,)\chi_{2898}(97,\cdot) χ2898(475,)\chi_{2898}(475,\cdot) χ2898(517,)\chi_{2898}(517,\cdot) χ2898(727,)\chi_{2898}(727,\cdot) χ2898(769,)\chi_{2898}(769,\cdot) χ2898(895,)\chi_{2898}(895,\cdot) χ2898(1147,)\chi_{2898}(1147,\cdot) χ2898(1399,)\chi_{2898}(1399,\cdot) χ2898(1483,)\chi_{2898}(1483,\cdot) χ2898(1525,)\chi_{2898}(1525,\cdot) χ2898(1735,)\chi_{2898}(1735,\cdot) χ2898(1861,)\chi_{2898}(1861,\cdot) χ2898(1903,)\chi_{2898}(1903,\cdot) χ2898(2029,)\chi_{2898}(2029,\cdot) χ2898(2113,)\chi_{2898}(2113,\cdot) χ2898(2365,)\chi_{2898}(2365,\cdot) χ2898(2407,)\chi_{2898}(2407,\cdot) χ2898(2491,)\chi_{2898}(2491,\cdot) χ2898(2659,)\chi_{2898}(2659,\cdot) χ2898(2869,)\chi_{2898}(2869,\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(13),1,e(722))(e\left(\frac{1}{3}\right),-1,e\left(\frac{7}{22}\right))

First values

aa 1-11155111113131717191925252929313137374141
χ2898(1903,a) \chi_{ 2898 }(1903, a) 1111e(1633)e\left(\frac{16}{33}\right)e(1366)e\left(\frac{13}{66}\right)e(4166)e\left(\frac{41}{66}\right)e(811)e\left(\frac{8}{11}\right)e(311)e\left(\frac{3}{11}\right)e(3233)e\left(\frac{32}{33}\right)e(233)e\left(\frac{2}{33}\right)e(566)e\left(\frac{5}{66}\right)e(1522)e\left(\frac{15}{22}\right)e(6566)e\left(\frac{65}{66}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2898(1903,a)   \chi_{ 2898 }(1903,a) \; at   a=\;a = e.g. 2