Properties

Conductor 2001
Order 44
Real No
Primitive No
Parity Even
Orbit Label 6003.cb

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(6003)
 
sage: chi = H[215]
 
pari: [g,chi] = znchar(Mod(215,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2001
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 44
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 = 6003.cb
Orbit index = 54

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 ]
 

\(\chi_{6003}(215,\cdot)\) \(\chi_{6003}(278,\cdot)\) \(\chi_{6003}(476,\cdot)\) \(\chi_{6003}(800,\cdot)\) \(\chi_{6003}(998,\cdot)\) \(\chi_{6003}(1061,\cdot)\) \(\chi_{6003}(1520,\cdot)\) \(\chi_{6003}(1844,\cdot)\) \(\chi_{6003}(2042,\cdot)\) \(\chi_{6003}(2105,\cdot)\) \(\chi_{6003}(2303,\cdot)\) \(\chi_{6003}(2888,\cdot)\) \(\chi_{6003}(3086,\cdot)\) \(\chi_{6003}(3347,\cdot)\) \(\chi_{6003}(3410,\cdot)\) \(\chi_{6003}(4130,\cdot)\) \(\chi_{6003}(4652,\cdot)\) \(\chi_{6003}(4976,\cdot)\) \(\chi_{6003}(5237,\cdot)\) \(\chi_{6003}(5759,\cdot)\)

Inducing primitive character

\(\chi_{2001}(215,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((-1,e\left(\frac{3}{11}\right),i)\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{25}{44}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{2}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{44})\)