Properties

Label 4050.203
Modulus 40504050
Conductor 20252025
Order 540540
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(4050, base_ring=CyclotomicField(540)) M = H._module chi = DirichletCharacter(H, M([530,189]))
 
Copy content pari:[g,chi] = znchar(Mod(203,4050))
 

Basic properties

Modulus: 40504050
Conductor: 20252025
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 540540
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from χ2025(203,)\chi_{2025}(203,\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 4050.bv

χ4050(23,)\chi_{4050}(23,\cdot) χ4050(47,)\chi_{4050}(47,\cdot) χ4050(77,)\chi_{4050}(77,\cdot) χ4050(83,)\chi_{4050}(83,\cdot) χ4050(113,)\chi_{4050}(113,\cdot) χ4050(137,)\chi_{4050}(137,\cdot) χ4050(167,)\chi_{4050}(167,\cdot) χ4050(173,)\chi_{4050}(173,\cdot) χ4050(203,)\chi_{4050}(203,\cdot) χ4050(227,)\chi_{4050}(227,\cdot) χ4050(263,)\chi_{4050}(263,\cdot) χ4050(317,)\chi_{4050}(317,\cdot) χ4050(347,)\chi_{4050}(347,\cdot) χ4050(353,)\chi_{4050}(353,\cdot) χ4050(383,)\chi_{4050}(383,\cdot) χ4050(437,)\chi_{4050}(437,\cdot) χ4050(473,)\chi_{4050}(473,\cdot) χ4050(497,)\chi_{4050}(497,\cdot) χ4050(527,)\chi_{4050}(527,\cdot) χ4050(533,)\chi_{4050}(533,\cdot) χ4050(563,)\chi_{4050}(563,\cdot) χ4050(587,)\chi_{4050}(587,\cdot) χ4050(617,)\chi_{4050}(617,\cdot) χ4050(623,)\chi_{4050}(623,\cdot) χ4050(653,)\chi_{4050}(653,\cdot) χ4050(677,)\chi_{4050}(677,\cdot) χ4050(713,)\chi_{4050}(713,\cdot) χ4050(767,)\chi_{4050}(767,\cdot) χ4050(797,)\chi_{4050}(797,\cdot) χ4050(803,)\chi_{4050}(803,\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(ζ540)\Q(\zeta_{540})
Fixed field: Number field defined by a degree 540 polynomial (not computed)

Values on generators

(2351,3727)(2351,3727)(e(5354),e(720))(e\left(\frac{53}{54}\right),e\left(\frac{7}{20}\right))

First values

aa 1-11177111113131717191923232929313137374141
χ4050(203,a) \chi_{ 4050 }(203, a) 1111e(49108)e\left(\frac{49}{108}\right)e(97270)e\left(\frac{97}{270}\right)e(271540)e\left(\frac{271}{540}\right)e(169180)e\left(\frac{169}{180}\right)e(3790)e\left(\frac{37}{90}\right)e(349540)e\left(\frac{349}{540}\right)e(2135)e\left(\frac{2}{135}\right)e(58135)e\left(\frac{58}{135}\right)e(67180)e\left(\frac{67}{180}\right)e(113270)e\left(\frac{113}{270}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ4050(203,a)   \chi_{ 4050 }(203,a) \; at   a=\;a = e.g. 2