Properties

Label 85600.19
Modulus 8560085600
Conductor 8560085600
Order 21202120
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(85600, base_ring=CyclotomicField(2120)) M = H._module chi = DirichletCharacter(H, M([1060,1855,1908,1560]))
 
Copy content pari:[g,chi] = znchar(Mod(19,85600))
 

Basic properties

Modulus: 8560085600
Conductor: 8560085600
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 21202120
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 85600.ii

χ85600(19,)\chi_{85600}(19,\cdot) χ85600(539,)\chi_{85600}(539,\cdot) χ85600(579,)\chi_{85600}(579,\cdot) χ85600(779,)\chi_{85600}(779,\cdot) χ85600(859,)\chi_{85600}(859,\cdot) χ85600(939,)\chi_{85600}(939,\cdot) χ85600(979,)\chi_{85600}(979,\cdot) χ85600(1019,)\chi_{85600}(1019,\cdot) χ85600(1139,)\chi_{85600}(1139,\cdot) χ85600(1219,)\chi_{85600}(1219,\cdot) χ85600(1539,)\chi_{85600}(1539,\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(ζ2120)\Q(\zeta_{2120})
Fixed field: Number field defined by a degree 2120 polynomial (not computed)

Values on generators

(26751,32101,82177,16801)(26751,32101,82177,16801)(1,e(78),e(910),e(3953))(-1,e\left(\frac{7}{8}\right),e\left(\frac{9}{10}\right),e\left(\frac{39}{53}\right))

First values

aa 1-1113377991111131317171919212123232727
χ85600(19,a) \chi_{ 85600 }(19, a) 1-111e(19812120)e\left(\frac{1981}{2120}\right)e(83212)e\left(\frac{83}{212}\right)e(9211060)e\left(\frac{921}{1060}\right)e(9832120)e\left(\frac{983}{2120}\right)e(11172120)e\left(\frac{1117}{2120}\right)e(143265)e\left(\frac{143}{265}\right)e(4692120)e\left(\frac{469}{2120}\right)e(6912120)e\left(\frac{691}{2120}\right)e(2891060)e\left(\frac{289}{1060}\right)e(17032120)e\left(\frac{1703}{2120}\right)
Copy content sage:chi.jacobi_sum(n)
 
χ85600(19,a)   \chi_{ 85600 }(19,a) \; at   a=\;a = e.g. 2