Properties

Label 2835.2774
Modulus 28352835
Conductor 28352835
Order 5454
Real no
Primitive yes
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(2835, base_ring=CyclotomicField(54)) M = H._module chi = DirichletCharacter(H, M([25,27,18]))
 
Copy content pari:[g,chi] = znchar(Mod(2774,2835))
 

Basic properties

Modulus: 28352835
Conductor: 28352835
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 5454
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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 2835.ei

χ2835(254,)\chi_{2835}(254,\cdot) χ2835(284,)\chi_{2835}(284,\cdot) χ2835(569,)\chi_{2835}(569,\cdot) χ2835(599,)\chi_{2835}(599,\cdot) χ2835(884,)\chi_{2835}(884,\cdot) χ2835(914,)\chi_{2835}(914,\cdot) χ2835(1199,)\chi_{2835}(1199,\cdot) χ2835(1229,)\chi_{2835}(1229,\cdot) χ2835(1514,)\chi_{2835}(1514,\cdot) χ2835(1544,)\chi_{2835}(1544,\cdot) χ2835(1829,)\chi_{2835}(1829,\cdot) χ2835(1859,)\chi_{2835}(1859,\cdot) χ2835(2144,)\chi_{2835}(2144,\cdot) χ2835(2174,)\chi_{2835}(2174,\cdot) χ2835(2459,)\chi_{2835}(2459,\cdot) χ2835(2489,)\chi_{2835}(2489,\cdot) χ2835(2774,)\chi_{2835}(2774,\cdot) χ2835(2804,)\chi_{2835}(2804,\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(ζ27)\Q(\zeta_{27})
Fixed field: Number field defined by a degree 54 polynomial

Values on generators

(1541,1702,2026)(1541,1702,2026)(e(2554),1,e(13))(e\left(\frac{25}{54}\right),-1,e\left(\frac{1}{3}\right))

First values

aa 1-1112244881111131316161717191922222323
χ2835(2774,a) \chi_{ 2835 }(2774, a) 1-111e(1727)e\left(\frac{17}{27}\right)e(727)e\left(\frac{7}{27}\right)e(89)e\left(\frac{8}{9}\right)e(1954)e\left(\frac{19}{54}\right)e(1154)e\left(\frac{11}{54}\right)e(1427)e\left(\frac{14}{27}\right)e(19)e\left(\frac{1}{9}\right)e(89)e\left(\frac{8}{9}\right)e(5354)e\left(\frac{53}{54}\right)e(727)e\left(\frac{7}{27}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ2835(2774,a)   \chi_{ 2835 }(2774,a) \; at   a=\;a = e.g. 2