Properties

Conductor 349
Order 174
Real No
Primitive No
Parity Even
Orbit Label 8027.bg

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(8027)
 
sage: chi = H[70]
 
pari: [g,chi] = znchar(Mod(70,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 349
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 174
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 = 8027.bg
Orbit index = 33

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 ]
 

\(\chi_{8027}(70,\cdot)\) \(\chi_{8027}(93,\cdot)\) \(\chi_{8027}(323,\cdot)\) \(\chi_{8027}(553,\cdot)\) \(\chi_{8027}(1151,\cdot)\) \(\chi_{8027}(1381,\cdot)\) \(\chi_{8027}(1565,\cdot)\) \(\chi_{8027}(1634,\cdot)\) \(\chi_{8027}(1726,\cdot)\) \(\chi_{8027}(1749,\cdot)\) \(\chi_{8027}(1818,\cdot)\) \(\chi_{8027}(1887,\cdot)\) \(\chi_{8027}(2071,\cdot)\) \(\chi_{8027}(2485,\cdot)\) \(\chi_{8027}(2600,\cdot)\) \(\chi_{8027}(2715,\cdot)\) \(\chi_{8027}(2922,\cdot)\) \(\chi_{8027}(2945,\cdot)\) \(\chi_{8027}(3060,\cdot)\) \(\chi_{8027}(3129,\cdot)\) \(\chi_{8027}(3198,\cdot)\) \(\chi_{8027}(3382,\cdot)\) \(\chi_{8027}(3405,\cdot)\) \(\chi_{8027}(3474,\cdot)\) \(\chi_{8027}(3566,\cdot)\) \(\chi_{8027}(3681,\cdot)\) \(\chi_{8027}(3704,\cdot)\) \(\chi_{8027}(3819,\cdot)\) \(\chi_{8027}(3842,\cdot)\) \(\chi_{8027}(3888,\cdot)\) ...

Inducing primitive character

\(\chi_{349}(70,\cdot)\)

Values on generators

\((350,5935)\) → \((1,e\left(\frac{17}{174}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{17}{174}\right)\)\(e\left(\frac{47}{87}\right)\)\(e\left(\frac{17}{87}\right)\)\(e\left(\frac{59}{87}\right)\)\(e\left(\frac{37}{58}\right)\)\(e\left(\frac{95}{174}\right)\)\(e\left(\frac{17}{58}\right)\)\(e\left(\frac{7}{87}\right)\)\(e\left(\frac{45}{58}\right)\)\(e\left(\frac{3}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{87})\)