Properties

Label 1254.41
Modulus 12541254
Conductor 627627
Order 9090
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(1254, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([45,27,65]))
 
Copy content pari:[g,chi] = znchar(Mod(41,1254))
 

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(41,)\chi_{627}(41,\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 1254.bq

χ1254(29,)\chi_{1254}(29,\cdot) χ1254(41,)\chi_{1254}(41,\cdot) χ1254(167,)\chi_{1254}(167,\cdot) χ1254(173,)\chi_{1254}(173,\cdot) χ1254(281,)\chi_{1254}(281,\cdot) χ1254(299,)\chi_{1254}(299,\cdot) χ1254(371,)\chi_{1254}(371,\cdot) χ1254(413,)\chi_{1254}(413,\cdot) χ1254(431,)\chi_{1254}(431,\cdot) χ1254(497,)\chi_{1254}(497,\cdot) χ1254(545,)\chi_{1254}(545,\cdot) χ1254(611,)\chi_{1254}(611,\cdot) χ1254(623,)\chi_{1254}(623,\cdot) χ1254(629,)\chi_{1254}(629,\cdot) χ1254(743,)\chi_{1254}(743,\cdot) χ1254(755,)\chi_{1254}(755,\cdot) χ1254(827,)\chi_{1254}(827,\cdot) χ1254(887,)\chi_{1254}(887,\cdot) χ1254(941,)\chi_{1254}(941,\cdot) χ1254(953,)\chi_{1254}(953,\cdot) χ1254(965,)\chi_{1254}(965,\cdot) χ1254(1085,)\chi_{1254}(1085,\cdot) χ1254(1097,)\chi_{1254}(1097,\cdot) χ1254(1229,)\chi_{1254}(1229,\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(310),e(1318))(-1,e\left(\frac{3}{10}\right),e\left(\frac{13}{18}\right))

First values

aa 1-111557713131717232325252929313135353737
χ1254(41,a) \chi_{ 1254 }(41, a) 1-111e(2390)e\left(\frac{23}{90}\right)e(1330)e\left(\frac{13}{30}\right)e(4145)e\left(\frac{41}{45}\right)e(1945)e\left(\frac{19}{45}\right)e(1718)e\left(\frac{17}{18}\right)e(2345)e\left(\frac{23}{45}\right)e(7990)e\left(\frac{79}{90}\right)e(1930)e\left(\frac{19}{30}\right)e(3145)e\left(\frac{31}{45}\right)e(110)e\left(\frac{1}{10}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ1254(41,a)   \chi_{ 1254 }(41,a) \; at   a=\;a = e.g. 2