Properties

Conductor 473
Order 70
Real No
Primitive No
Parity Even
Orbit Label 8041.dt

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(8041)
 
sage: chi = H[409]
 
pari: [g,chi] = znchar(Mod(409,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 70
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.dt
Orbit index = 98

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{8041}(409,\cdot)\) \(\chi_{8041}(426,\cdot)\) \(\chi_{8041}(1140,\cdot)\) \(\chi_{8041}(1157,\cdot)\) \(\chi_{8041}(1888,\cdot)\) \(\chi_{8041}(2109,\cdot)\) \(\chi_{8041}(2483,\cdot)\) \(\chi_{8041}(2602,\cdot)\) \(\chi_{8041}(2840,\cdot)\) \(\chi_{8041}(3214,\cdot)\) \(\chi_{8041}(3350,\cdot)\) \(\chi_{8041}(3571,\cdot)\) \(\chi_{8041}(3792,\cdot)\) \(\chi_{8041}(3945,\cdot)\) \(\chi_{8041}(4523,\cdot)\) \(\chi_{8041}(5033,\cdot)\) \(\chi_{8041}(5101,\cdot)\) \(\chi_{8041}(5254,\cdot)\) \(\chi_{8041}(5407,\cdot)\) \(\chi_{8041}(5832,\cdot)\) \(\chi_{8041}(6563,\cdot)\) \(\chi_{8041}(6716,\cdot)\) \(\chi_{8041}(7719,\cdot)\) \(\chi_{8041}(8025,\cdot)\)

Inducing primitive character

\(\chi_{473}(409,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{10}\right),1,e\left(\frac{5}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{11}{70}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{23}{70}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{8}{35}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{9}{14}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)