Properties

Conductor 667
Order 154
Real No
Primitive No
Parity Even
Orbit Label 6003.cy

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[64]
 
pari: [g,chi] = znchar(Mod(64,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 667
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.cy
Orbit index = 77

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 ]
 

\(\chi_{6003}(64,\cdot)\) \(\chi_{6003}(100,\cdot)\) \(\chi_{6003}(154,\cdot)\) \(\chi_{6003}(325,\cdot)\) \(\chi_{6003}(361,\cdot)\) \(\chi_{6003}(370,\cdot)\) \(\chi_{6003}(469,\cdot)\) \(\chi_{6003}(676,\cdot)\) \(\chi_{6003}(883,\cdot)\) \(\chi_{6003}(892,\cdot)\) \(\chi_{6003}(991,\cdot)\) \(\chi_{6003}(1108,\cdot)\) \(\chi_{6003}(1135,\cdot)\) \(\chi_{6003}(1153,\cdot)\) \(\chi_{6003}(1198,\cdot)\) \(\chi_{6003}(1369,\cdot)\) \(\chi_{6003}(1396,\cdot)\) \(\chi_{6003}(1405,\cdot)\) \(\chi_{6003}(1513,\cdot)\) \(\chi_{6003}(1720,\cdot)\) \(\chi_{6003}(1774,\cdot)\) \(\chi_{6003}(1918,\cdot)\) \(\chi_{6003}(1927,\cdot)\) \(\chi_{6003}(1936,\cdot)\) \(\chi_{6003}(1981,\cdot)\) \(\chi_{6003}(2152,\cdot)\) \(\chi_{6003}(2188,\cdot)\) \(\chi_{6003}(2197,\cdot)\) \(\chi_{6003}(2440,\cdot)\) \(\chi_{6003}(2557,\cdot)\) ...

Inducing primitive character

\(\chi_{667}(64,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((1,e\left(\frac{6}{11}\right),e\left(\frac{3}{14}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{47}{154}\right)\)\(e\left(\frac{47}{77}\right)\)\(e\left(\frac{20}{77}\right)\)\(e\left(\frac{72}{77}\right)\)\(e\left(\frac{141}{154}\right)\)\(e\left(\frac{87}{154}\right)\)\(e\left(\frac{41}{154}\right)\)\(e\left(\frac{38}{77}\right)\)\(e\left(\frac{37}{154}\right)\)\(e\left(\frac{17}{77}\right)\)
value at  e.g. 2

Related number fields

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