Properties

Label 2898.95
Modulus 28982898
Conductor 14491449
Order 6666
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Downloads

Learn more

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([55,44,48]))
 
Copy content pari:[g,chi] = znchar(Mod(95,2898))
 

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(95,)\chi_{1449}(95,\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.db

χ2898(95,)\chi_{2898}(95,\cdot) χ2898(317,)\chi_{2898}(317,\cdot) χ2898(347,)\chi_{2898}(347,\cdot) χ2898(443,)\chi_{2898}(443,\cdot) χ2898(473,)\chi_{2898}(473,\cdot) χ2898(725,)\chi_{2898}(725,\cdot) χ2898(821,)\chi_{2898}(821,\cdot) χ2898(947,)\chi_{2898}(947,\cdot) χ2898(1199,)\chi_{2898}(1199,\cdot) χ2898(1451,)\chi_{2898}(1451,\cdot) χ2898(1481,)\chi_{2898}(1481,\cdot) χ2898(1577,)\chi_{2898}(1577,\cdot) χ2898(1733,)\chi_{2898}(1733,\cdot) χ2898(1829,)\chi_{2898}(1829,\cdot) χ2898(2111,)\chi_{2898}(2111,\cdot) χ2898(2237,)\chi_{2898}(2237,\cdot) χ2898(2585,)\chi_{2898}(2585,\cdot) χ2898(2615,)\chi_{2898}(2615,\cdot) χ2898(2741,)\chi_{2898}(2741,\cdot) χ2898(2837,)\chi_{2898}(2837,\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(56),e(23),e(811))(e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{8}{11}\right))

First values

aa 1-11155111113131717191925252929313137374141
χ2898(95,a) \chi_{ 2898 }(95, a) 1-111e(522)e\left(\frac{5}{22}\right)e(122)e\left(\frac{1}{22}\right)e(2833)e\left(\frac{28}{33}\right)e(1766)e\left(\frac{17}{66}\right)e(833)e\left(\frac{8}{33}\right)e(511)e\left(\frac{5}{11}\right)e(6166)e\left(\frac{61}{66}\right)e(2333)e\left(\frac{23}{33}\right)e(2033)e\left(\frac{20}{33}\right)e(5966)e\left(\frac{59}{66}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2898(95,a)   \chi_{ 2898 }(95,a) \; at   a=\;a = e.g. 2