Properties

Conductor 207
Order 33
Real No
Primitive No
Parity Even
Orbit Label 6003.bt

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[349]
 
pari: [g,chi] = znchar(Mod(349,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 207
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 33
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.bt
Orbit index = 46

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 ]
 

\(\chi_{6003}(349,\cdot)\) \(\chi_{6003}(610,\cdot)\) \(\chi_{6003}(1393,\cdot)\) \(\chi_{6003}(1480,\cdot)\) \(\chi_{6003}(1741,\cdot)\) \(\chi_{6003}(1915,\cdot)\) \(\chi_{6003}(2263,\cdot)\) \(\chi_{6003}(2785,\cdot)\) \(\chi_{6003}(3307,\cdot)\) \(\chi_{6003}(3481,\cdot)\) \(\chi_{6003}(3568,\cdot)\) \(\chi_{6003}(3742,\cdot)\) \(\chi_{6003}(4264,\cdot)\) \(\chi_{6003}(4351,\cdot)\) \(\chi_{6003}(4612,\cdot)\) \(\chi_{6003}(4786,\cdot)\) \(\chi_{6003}(5308,\cdot)\) \(\chi_{6003}(5395,\cdot)\) \(\chi_{6003}(5569,\cdot)\) \(\chi_{6003}(5917,\cdot)\)

Inducing primitive character

\(\chi_{207}(142,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{2}{11}\right),1)\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{10}{33}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{4}{33}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)