Properties

Label 1254.347
Modulus 12541254
Conductor 627627
Order 9090
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(1254, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([45,81,80]))
 
Copy content pari:[g,chi] = znchar(Mod(347,1254))
 

Basic properties

Modulus: 12541254
Conductor: 627627
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 9090
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ627(347,)\chi_{627}(347,\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 1254.br

χ1254(17,)\chi_{1254}(17,\cdot) χ1254(35,)\chi_{1254}(35,\cdot) χ1254(101,)\chi_{1254}(101,\cdot) χ1254(149,)\chi_{1254}(149,\cdot) χ1254(161,)\chi_{1254}(161,\cdot) χ1254(215,)\chi_{1254}(215,\cdot) χ1254(233,)\chi_{1254}(233,\cdot) χ1254(347,)\chi_{1254}(347,\cdot) χ1254(359,)\chi_{1254}(359,\cdot) χ1254(365,)\chi_{1254}(365,\cdot) χ1254(479,)\chi_{1254}(479,\cdot) χ1254(491,)\chi_{1254}(491,\cdot) χ1254(503,)\chi_{1254}(503,\cdot) χ1254(557,)\chi_{1254}(557,\cdot) χ1254(689,)\chi_{1254}(689,\cdot) χ1254(701,)\chi_{1254}(701,\cdot) χ1254(821,)\chi_{1254}(821,\cdot) χ1254(833,)\chi_{1254}(833,\cdot) χ1254(899,)\chi_{1254}(899,\cdot) χ1254(959,)\chi_{1254}(959,\cdot) χ1254(1031,)\chi_{1254}(1031,\cdot) χ1254(1073,)\chi_{1254}(1073,\cdot) χ1254(1157,)\chi_{1254}(1157,\cdot) χ1254(1163,)\chi_{1254}(1163,\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(ζ45)\Q(\zeta_{45})
Fixed field: Number field defined by a degree 90 polynomial

Values on generators

(419,343,1123)(419,343,1123)(1,e(910),e(89))(-1,e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))

First values

aa 1-111557713131717232325252929313135353737
χ1254(347,a) \chi_{ 1254 }(347, a) 1111e(2990)e\left(\frac{29}{90}\right)e(1930)e\left(\frac{19}{30}\right)e(3190)e\left(\frac{31}{90}\right)e(2245)e\left(\frac{22}{45}\right)e(518)e\left(\frac{5}{18}\right)e(2945)e\left(\frac{29}{45}\right)e(4145)e\left(\frac{41}{45}\right)e(1115)e\left(\frac{11}{15}\right)e(4345)e\left(\frac{43}{45}\right)e(45)e\left(\frac{4}{5}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ1254(347,a)   \chi_{ 1254 }(347,a) \; at   a=\;a = e.g. 2