Properties

Label 9200.1881
Modulus 92009200
Conductor 46004600
Order 110110
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9200, base_ring=CyclotomicField(110)) M = H._module chi = DirichletCharacter(H, M([0,55,44,60]))
 
Copy content pari:[g,chi] = znchar(Mod(1881,9200))
 

Basic properties

Modulus: 92009200
Conductor: 46004600
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 110110
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ4600(4181,)\chi_{4600}(4181,\cdot)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 9200.er

χ9200(41,)\chi_{9200}(41,\cdot) χ9200(121,)\chi_{9200}(121,\cdot) χ9200(361,)\chi_{9200}(361,\cdot) χ9200(441,)\chi_{9200}(441,\cdot) χ9200(761,)\chi_{9200}(761,\cdot) χ9200(841,)\chi_{9200}(841,\cdot) χ9200(1481,)\chi_{9200}(1481,\cdot) χ9200(1641,)\chi_{9200}(1641,\cdot) χ9200(1881,)\chi_{9200}(1881,\cdot) χ9200(1961,)\chi_{9200}(1961,\cdot) χ9200(2281,)\chi_{9200}(2281,\cdot) χ9200(2441,)\chi_{9200}(2441,\cdot) χ9200(2681,)\chi_{9200}(2681,\cdot) χ9200(2841,)\chi_{9200}(2841,\cdot) χ9200(3321,)\chi_{9200}(3321,\cdot) χ9200(3481,)\chi_{9200}(3481,\cdot) χ9200(3721,)\chi_{9200}(3721,\cdot) χ9200(4041,)\chi_{9200}(4041,\cdot) χ9200(4121,)\chi_{9200}(4121,\cdot) χ9200(4281,)\chi_{9200}(4281,\cdot) χ9200(4441,)\chi_{9200}(4441,\cdot) χ9200(4521,)\chi_{9200}(4521,\cdot) χ9200(4681,)\chi_{9200}(4681,\cdot) χ9200(5161,)\chi_{9200}(5161,\cdot) χ9200(5321,)\chi_{9200}(5321,\cdot) χ9200(5561,)\chi_{9200}(5561,\cdot) χ9200(5641,)\chi_{9200}(5641,\cdot) χ9200(5881,)\chi_{9200}(5881,\cdot) χ9200(5961,)\chi_{9200}(5961,\cdot) χ9200(6121,)\chi_{9200}(6121,\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(ζ55)\Q(\zeta_{55})
Fixed field: Number field defined by a degree 110 polynomial (not computed)

Values on generators

(1151,6901,2577,1201)(1151,6901,2577,1201)(1,1,e(25),e(611))(1,-1,e\left(\frac{2}{5}\right),e\left(\frac{6}{11}\right))

First values

aa 1-1113377991111131317171919212127272929
χ9200(1881,a) \chi_{ 9200 }(1881, a) 1111e(3110)e\left(\frac{3}{110}\right)e(411)e\left(\frac{4}{11}\right)e(355)e\left(\frac{3}{55}\right)e(89110)e\left(\frac{89}{110}\right)e(81110)e\left(\frac{81}{110}\right)e(155)e\left(\frac{1}{55}\right)e(97110)e\left(\frac{97}{110}\right)e(43110)e\left(\frac{43}{110}\right)e(9110)e\left(\frac{9}{110}\right)e(13110)e\left(\frac{13}{110}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ9200(1881,a)   \chi_{ 9200 }(1881,a) \; at   a=\;a = e.g. 2