Properties

Conductor 23
Order 11
Real No
Primitive No
Parity Even
Orbit Label 8027.k

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[699]
 
pari: [g,chi] = znchar(Mod(699,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 23
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 11
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.k
Orbit index = 11

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 ]
 

\(\chi_{8027}(699,\cdot)\) \(\chi_{8027}(1048,\cdot)\) \(\chi_{8027}(2095,\cdot)\) \(\chi_{8027}(2444,\cdot)\) \(\chi_{8027}(3491,\cdot)\) \(\chi_{8027}(4189,\cdot)\) \(\chi_{8027}(6283,\cdot)\) \(\chi_{8027}(6632,\cdot)\) \(\chi_{8027}(6981,\cdot)\) \(\chi_{8027}(7330,\cdot)\)

Inducing primitive character

\(\chi_{23}(9,\cdot)\)

Values on generators

\((350,5935)\) → \((e\left(\frac{5}{11}\right),1)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{1}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{11})\)