Properties

Conductor 349
Order 87
Real No
Primitive No
Parity Even
Orbit Label 8027.ba

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[116]
 
pari: [g,chi] = znchar(Mod(116,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 349
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 87
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.ba
Orbit index = 27

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 ]
 

\(\chi_{8027}(116,\cdot)\) \(\chi_{8027}(185,\cdot)\) \(\chi_{8027}(254,\cdot)\) \(\chi_{8027}(300,\cdot)\) \(\chi_{8027}(346,\cdot)\) \(\chi_{8027}(369,\cdot)\) \(\chi_{8027}(484,\cdot)\) \(\chi_{8027}(507,\cdot)\) \(\chi_{8027}(622,\cdot)\) \(\chi_{8027}(714,\cdot)\) \(\chi_{8027}(783,\cdot)\) \(\chi_{8027}(806,\cdot)\) \(\chi_{8027}(990,\cdot)\) \(\chi_{8027}(1059,\cdot)\) \(\chi_{8027}(1128,\cdot)\) \(\chi_{8027}(1243,\cdot)\) \(\chi_{8027}(1266,\cdot)\) \(\chi_{8027}(1473,\cdot)\) \(\chi_{8027}(1588,\cdot)\) \(\chi_{8027}(1703,\cdot)\) \(\chi_{8027}(2117,\cdot)\) \(\chi_{8027}(2301,\cdot)\) \(\chi_{8027}(2370,\cdot)\) \(\chi_{8027}(2439,\cdot)\) \(\chi_{8027}(2462,\cdot)\) \(\chi_{8027}(2554,\cdot)\) \(\chi_{8027}(2623,\cdot)\) \(\chi_{8027}(2807,\cdot)\) \(\chi_{8027}(3037,\cdot)\) \(\chi_{8027}(3635,\cdot)\) ...

Inducing primitive character

\(\chi_{349}(116,\cdot)\)

Values on generators

\((350,5935)\) → \((1,e\left(\frac{37}{87}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{37}{87}\right)\)\(e\left(\frac{5}{87}\right)\)\(e\left(\frac{74}{87}\right)\)\(e\left(\frac{47}{87}\right)\)\(e\left(\frac{14}{29}\right)\)\(e\left(\frac{43}{87}\right)\)\(e\left(\frac{8}{29}\right)\)\(e\left(\frac{10}{87}\right)\)\(e\left(\frac{28}{29}\right)\)\(e\left(\frac{27}{29}\right)\)
value at  e.g. 2

Related number fields

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