Properties

Label 4334.149
Modulus 43344334
Conductor 21672167
Order 980980
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(4334, base_ring=CyclotomicField(980)) M = H._module chi = DirichletCharacter(H, M([882,435]))
 
Copy content pari:[g,chi] = znchar(Mod(149,4334))
 

Basic properties

Modulus: 43344334
Conductor: 21672167
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 980980
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ2167(149,)\chi_{2167}(149,\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 4334.bj

χ4334(13,)\chi_{4334}(13,\cdot) χ4334(17,)\chi_{4334}(17,\cdot) χ4334(35,)\chi_{4334}(35,\cdot) χ4334(57,)\chi_{4334}(57,\cdot) χ4334(73,)\chi_{4334}(73,\cdot) χ4334(79,)\chi_{4334}(79,\cdot) χ4334(95,)\chi_{4334}(95,\cdot) χ4334(117,)\chi_{4334}(117,\cdot) χ4334(123,)\chi_{4334}(123,\cdot) χ4334(139,)\chi_{4334}(139,\cdot) χ4334(145,)\chi_{4334}(145,\cdot) χ4334(149,)\chi_{4334}(149,\cdot) χ4334(151,)\chi_{4334}(151,\cdot) χ4334(167,)\chi_{4334}(167,\cdot) χ4334(189,)\chi_{4334}(189,\cdot) χ4334(195,)\chi_{4334}(195,\cdot) χ4334(205,)\chi_{4334}(205,\cdot) χ4334(215,)\chi_{4334}(215,\cdot) χ4334(227,)\chi_{4334}(227,\cdot) χ4334(249,)\chi_{4334}(249,\cdot) χ4334(255,)\chi_{4334}(255,\cdot) χ4334(271,)\chi_{4334}(271,\cdot) χ4334(277,)\chi_{4334}(277,\cdot) χ4334(283,)\chi_{4334}(283,\cdot) χ4334(299,)\chi_{4334}(299,\cdot) χ4334(303,)\chi_{4334}(303,\cdot) χ4334(305,)\chi_{4334}(305,\cdot) χ4334(315,)\chi_{4334}(315,\cdot) χ4334(321,)\chi_{4334}(321,\cdot) χ4334(327,)\chi_{4334}(327,\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(ζ980)\Q(\zeta_{980})
Fixed field: Number field defined by a degree 980 polynomial (not computed)

Values on generators

(1971,199)(1971,199)(e(910),e(87196))(e\left(\frac{9}{10}\right),e\left(\frac{87}{196}\right))

First values

aa 1-11133557799131315151717191921212323
χ4334(149,a) \chi_{ 4334 }(149, a) 1111e(531980)e\left(\frac{531}{980}\right)e(103980)e\left(\frac{103}{980}\right)e(26245)e\left(\frac{26}{245}\right)e(41490)e\left(\frac{41}{490}\right)e(977980)e\left(\frac{977}{980}\right)e(317490)e\left(\frac{317}{490}\right)e(663980)e\left(\frac{663}{980}\right)e(235)e\left(\frac{2}{35}\right)e(127196)e\left(\frac{127}{196}\right)e(1349)e\left(\frac{13}{49}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ4334(149,a)   \chi_{ 4334 }(149,a) \; at   a=\;a = e.g. 2