Properties

Conductor 667
Order 308
Real No
Primitive No
Parity Even
Orbit Label 6003.df

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[10]
 
pari: [g,chi] = znchar(Mod(10,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 667
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.df
Orbit index = 84

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 ]
 

\(\chi_{6003}(10,\cdot)\) \(\chi_{6003}(19,\cdot)\) \(\chi_{6003}(37,\cdot)\) \(\chi_{6003}(172,\cdot)\) \(\chi_{6003}(217,\cdot)\) \(\chi_{6003}(235,\cdot)\) \(\chi_{6003}(316,\cdot)\) \(\chi_{6003}(379,\cdot)\) \(\chi_{6003}(388,\cdot)\) \(\chi_{6003}(424,\cdot)\) \(\chi_{6003}(433,\cdot)\) \(\chi_{6003}(559,\cdot)\) \(\chi_{6003}(595,\cdot)\) \(\chi_{6003}(640,\cdot)\) \(\chi_{6003}(649,\cdot)\) \(\chi_{6003}(757,\cdot)\) \(\chi_{6003}(793,\cdot)\) \(\chi_{6003}(802,\cdot)\) \(\chi_{6003}(820,\cdot)\) \(\chi_{6003}(838,\cdot)\) \(\chi_{6003}(856,\cdot)\) \(\chi_{6003}(1000,\cdot)\) \(\chi_{6003}(1054,\cdot)\) \(\chi_{6003}(1063,\cdot)\) \(\chi_{6003}(1171,\cdot)\) \(\chi_{6003}(1207,\cdot)\) \(\chi_{6003}(1216,\cdot)\) \(\chi_{6003}(1261,\cdot)\) \(\chi_{6003}(1279,\cdot)\) \(\chi_{6003}(1378,\cdot)\) ...

Inducing primitive character

\(\chi_{667}(10,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((1,e\left(\frac{3}{22}\right),e\left(\frac{23}{28}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{29}{308}\right)\)\(e\left(\frac{29}{154}\right)\)\(e\left(\frac{16}{77}\right)\)\(e\left(\frac{69}{154}\right)\)\(e\left(\frac{87}{308}\right)\)\(e\left(\frac{93}{308}\right)\)\(e\left(\frac{235}{308}\right)\)\(e\left(\frac{107}{154}\right)\)\(e\left(\frac{167}{308}\right)\)\(e\left(\frac{29}{77}\right)\)
value at  e.g. 2

Related number fields

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