Properties

Label 4284.95
Modulus 42844284
Conductor 42844284
Order 4848
Real no
Primitive yes
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(4284, base_ring=CyclotomicField(48)) M = H._module chi = DirichletCharacter(H, M([24,40,32,9]))
 
Copy content pari:[g,chi] = znchar(Mod(95,4284))
 

Basic properties

Modulus: 42844284
Conductor: 42844284
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 4848
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
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 4284.ha

χ4284(95,)\chi_{4284}(95,\cdot) χ4284(347,)\chi_{4284}(347,\cdot) χ4284(947,)\chi_{4284}(947,\cdot) χ4284(1355,)\chi_{4284}(1355,\cdot) χ4284(1451,)\chi_{4284}(1451,\cdot) χ4284(1703,)\chi_{4284}(1703,\cdot) χ4284(1859,)\chi_{4284}(1859,\cdot) χ4284(2111,)\chi_{4284}(2111,\cdot) χ4284(2207,)\chi_{4284}(2207,\cdot) χ4284(2459,)\chi_{4284}(2459,\cdot) χ4284(2615,)\chi_{4284}(2615,\cdot) χ4284(2867,)\chi_{4284}(2867,\cdot) χ4284(2963,)\chi_{4284}(2963,\cdot) χ4284(3371,)\chi_{4284}(3371,\cdot) χ4284(3971,)\chi_{4284}(3971,\cdot) χ4284(4223,)\chi_{4284}(4223,\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(ζ48)\Q(\zeta_{48})
Fixed field: Number field defined by a degree 48 polynomial

Values on generators

(2143,3809,1837,1261)(2143,3809,1837,1261)(1,e(56),e(23),e(316))(-1,e\left(\frac{5}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{16}\right))

First values

aa 1-11155111113131919232325252929313137374141
χ4284(95,a) \chi_{ 4284 }(95, a) 1-111e(716)e\left(\frac{7}{16}\right)e(516)e\left(\frac{5}{16}\right)e(512)e\left(\frac{5}{12}\right)e(1124)e\left(\frac{11}{24}\right)e(1316)e\left(\frac{13}{16}\right)e(78)e\left(\frac{7}{8}\right)e(1348)e\left(\frac{13}{48}\right)e(2548)e\left(\frac{25}{48}\right)e(2548)e\left(\frac{25}{48}\right)e(1148)e\left(\frac{11}{48}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ4284(95,a)   \chi_{ 4284 }(95,a) \; at   a=\;a = e.g. 2