Properties

Conductor 2001
Order 308
Real No
Primitive No
Parity Even
Orbit Label 6003.dg

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[8]
 
pari: [g,chi] = znchar(Mod(8,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2001
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 308
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.dg
Orbit index = 85

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 ]
 

\(\chi_{6003}(8,\cdot)\) \(\chi_{6003}(26,\cdot)\) \(\chi_{6003}(98,\cdot)\) \(\chi_{6003}(188,\cdot)\) \(\chi_{6003}(242,\cdot)\) \(\chi_{6003}(269,\cdot)\) \(\chi_{6003}(305,\cdot)\) \(\chi_{6003}(395,\cdot)\) \(\chi_{6003}(404,\cdot)\) \(\chi_{6003}(449,\cdot)\) \(\chi_{6003}(485,\cdot)\) \(\chi_{6003}(512,\cdot)\) \(\chi_{6003}(611,\cdot)\) \(\chi_{6003}(656,\cdot)\) \(\chi_{6003}(791,\cdot)\) \(\chi_{6003}(809,\cdot)\) \(\chi_{6003}(926,\cdot)\) \(\chi_{6003}(1007,\cdot)\) \(\chi_{6003}(1025,\cdot)\) \(\chi_{6003}(1070,\cdot)\) \(\chi_{6003}(1133,\cdot)\) \(\chi_{6003}(1232,\cdot)\) \(\chi_{6003}(1250,\cdot)\) \(\chi_{6003}(1268,\cdot)\) \(\chi_{6003}(1313,\cdot)\) \(\chi_{6003}(1439,\cdot)\) \(\chi_{6003}(1511,\cdot)\) \(\chi_{6003}(1547,\cdot)\) \(\chi_{6003}(1664,\cdot)\) \(\chi_{6003}(1754,\cdot)\) ...

Inducing primitive character

\(\chi_{2001}(8,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((-1,e\left(\frac{3}{11}\right),e\left(\frac{3}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{47}{308}\right)\)\(e\left(\frac{47}{154}\right)\)\(e\left(\frac{10}{77}\right)\)\(e\left(\frac{36}{77}\right)\)\(e\left(\frac{141}{308}\right)\)\(e\left(\frac{87}{308}\right)\)\(e\left(\frac{195}{308}\right)\)\(e\left(\frac{115}{154}\right)\)\(e\left(\frac{191}{308}\right)\)\(e\left(\frac{47}{77}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{308})\)