Properties

Conductor 349
Order 58
Real No
Primitive No
Parity Even
Orbit Label 8027.v

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[139]
 
pari: [g,chi] = znchar(Mod(139,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 349
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 58
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.v
Orbit index = 22

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 ]
 

\(\chi_{8027}(139,\cdot)\) \(\chi_{8027}(231,\cdot)\) \(\chi_{8027}(530,\cdot)\) \(\chi_{8027}(921,\cdot)\) \(\chi_{8027}(1496,\cdot)\) \(\chi_{8027}(1657,\cdot)\) \(\chi_{8027}(1772,\cdot)\) \(\chi_{8027}(2163,\cdot)\) \(\chi_{8027}(2186,\cdot)\) \(\chi_{8027}(2209,\cdot)\) \(\chi_{8027}(2761,\cdot)\) \(\chi_{8027}(3221,\cdot)\) \(\chi_{8027}(3773,\cdot)\) \(\chi_{8027}(4233,\cdot)\) \(\chi_{8027}(4601,\cdot)\) \(\chi_{8027}(4923,\cdot)\) \(\chi_{8027}(4946,\cdot)\) \(\chi_{8027}(5360,\cdot)\) \(\chi_{8027}(5659,\cdot)\) \(\chi_{8027}(5705,\cdot)\) \(\chi_{8027}(5866,\cdot)\) \(\chi_{8027}(5981,\cdot)\) \(\chi_{8027}(6648,\cdot)\) \(\chi_{8027}(6717,\cdot)\) \(\chi_{8027}(6809,\cdot)\) \(\chi_{8027}(7016,\cdot)\) \(\chi_{8027}(7568,\cdot)\) \(\chi_{8027}(7637,\cdot)\)

Inducing primitive character

\(\chi_{349}(139,\cdot)\)

Values on generators

\((350,5935)\) → \((1,e\left(\frac{39}{58}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{39}{58}\right)\)\(e\left(\frac{14}{29}\right)\)\(e\left(\frac{10}{29}\right)\)\(e\left(\frac{4}{29}\right)\)\(e\left(\frac{9}{58}\right)\)\(e\left(\frac{3}{58}\right)\)\(e\left(\frac{1}{58}\right)\)\(e\left(\frac{28}{29}\right)\)\(e\left(\frac{47}{58}\right)\)\(e\left(\frac{7}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{29})\)