Properties

Conductor 667
Order 77
Real No
Primitive No
Parity Even
Orbit Label 6003.cm

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[82]
 
pari: [g,chi] = znchar(Mod(82,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 667
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 77
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.cm
Orbit index = 65

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 ]
 

\(\chi_{6003}(82,\cdot)\) \(\chi_{6003}(190,\cdot)\) \(\chi_{6003}(397,\cdot)\) \(\chi_{6003}(487,\cdot)\) \(\chi_{6003}(604,\cdot)\) \(\chi_{6003}(703,\cdot)\) \(\chi_{6003}(721,\cdot)\) \(\chi_{6003}(748,\cdot)\) \(\chi_{6003}(982,\cdot)\) \(\chi_{6003}(1225,\cdot)\) \(\chi_{6003}(1504,\cdot)\) \(\chi_{6003}(1531,\cdot)\) \(\chi_{6003}(1756,\cdot)\) \(\chi_{6003}(1963,\cdot)\) \(\chi_{6003}(2017,\cdot)\) \(\chi_{6003}(2026,\cdot)\) \(\chi_{6003}(2053,\cdot)\) \(\chi_{6003}(2170,\cdot)\) \(\chi_{6003}(2224,\cdot)\) \(\chi_{6003}(2431,\cdot)\) \(\chi_{6003}(2539,\cdot)\) \(\chi_{6003}(2548,\cdot)\) \(\chi_{6003}(2746,\cdot)\) \(\chi_{6003}(2791,\cdot)\) \(\chi_{6003}(2809,\cdot)\) \(\chi_{6003}(2953,\cdot)\) \(\chi_{6003}(3052,\cdot)\) \(\chi_{6003}(3061,\cdot)\) \(\chi_{6003}(3268,\cdot)\) \(\chi_{6003}(3475,\cdot)\) ...

Inducing primitive character

\(\chi_{667}(82,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((1,e\left(\frac{7}{11}\right),e\left(\frac{2}{7}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{43}{77}\right)\)\(e\left(\frac{9}{77}\right)\)\(e\left(\frac{71}{77}\right)\)\(e\left(\frac{40}{77}\right)\)\(e\left(\frac{52}{77}\right)\)\(e\left(\frac{37}{77}\right)\)\(e\left(\frac{67}{77}\right)\)\(e\left(\frac{4}{77}\right)\)\(e\left(\frac{6}{77}\right)\)\(e\left(\frac{18}{77}\right)\)
value at  e.g. 2

Related number fields

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