Properties

Conductor 2001
Order 154
Real No
Primitive No
Parity Even
Orbit Label 6003.cx

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[53]
 
pari: [g,chi] = znchar(Mod(53,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2001
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 154
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.cx
Orbit index = 76

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 ]
 

\(\chi_{6003}(53,\cdot)\) \(\chi_{6003}(107,\cdot)\) \(\chi_{6003}(152,\cdot)\) \(\chi_{6003}(314,\cdot)\) \(\chi_{6003}(431,\cdot)\) \(\chi_{6003}(458,\cdot)\) \(\chi_{6003}(674,\cdot)\) \(\chi_{6003}(935,\cdot)\) \(\chi_{6003}(953,\cdot)\) \(\chi_{6003}(980,\cdot)\) \(\chi_{6003}(1466,\cdot)\) \(\chi_{6003}(1502,\cdot)\) \(\chi_{6003}(1673,\cdot)\) \(\chi_{6003}(1736,\cdot)\) \(\chi_{6003}(1763,\cdot)\) \(\chi_{6003}(1880,\cdot)\) \(\chi_{6003}(1988,\cdot)\) \(\chi_{6003}(1997,\cdot)\) \(\chi_{6003}(2195,\cdot)\) \(\chi_{6003}(2402,\cdot)\) \(\chi_{6003}(2501,\cdot)\) \(\chi_{6003}(2771,\cdot)\) \(\chi_{6003}(2780,\cdot)\) \(\chi_{6003}(2978,\cdot)\) \(\chi_{6003}(3023,\cdot)\) \(\chi_{6003}(3032,\cdot)\) \(\chi_{6003}(3041,\cdot)\) \(\chi_{6003}(3185,\cdot)\) \(\chi_{6003}(3239,\cdot)\) \(\chi_{6003}(3329,\cdot)\) ...

Inducing primitive character

\(\chi_{2001}(53,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((-1,e\left(\frac{19}{22}\right),e\left(\frac{2}{7}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{79}{154}\right)\)\(e\left(\frac{2}{77}\right)\)\(e\left(\frac{50}{77}\right)\)\(e\left(\frac{129}{154}\right)\)\(e\left(\frac{83}{154}\right)\)\(e\left(\frac{25}{154}\right)\)\(e\left(\frac{32}{77}\right)\)\(e\left(\frac{18}{77}\right)\)\(e\left(\frac{27}{77}\right)\)\(e\left(\frac{4}{77}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{77})\)