Properties

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

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[80]
 
pari: [g,chi] = znchar(Mod(80,6003))
 

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.db
Orbit index = 80

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 ]
 

\(\chi_{6003}(80,\cdot)\) \(\chi_{6003}(125,\cdot)\) \(\chi_{6003}(296,\cdot)\) \(\chi_{6003}(332,\cdot)\) \(\chi_{6003}(341,\cdot)\) \(\chi_{6003}(557,\cdot)\) \(\chi_{6003}(701,\cdot)\) \(\chi_{6003}(845,\cdot)\) \(\chi_{6003}(908,\cdot)\) \(\chi_{6003}(962,\cdot)\) \(\chi_{6003}(1079,\cdot)\) \(\chi_{6003}(1115,\cdot)\) \(\chi_{6003}(1124,\cdot)\) \(\chi_{6003}(1169,\cdot)\) \(\chi_{6003}(1367,\cdot)\) \(\chi_{6003}(1376,\cdot)\) \(\chi_{6003}(1385,\cdot)\) \(\chi_{6003}(1601,\cdot)\) \(\chi_{6003}(1745,\cdot)\) \(\chi_{6003}(1907,\cdot)\) \(\chi_{6003}(1952,\cdot)\) \(\chi_{6003}(2006,\cdot)\) \(\chi_{6003}(2123,\cdot)\) \(\chi_{6003}(2150,\cdot)\) \(\chi_{6003}(2159,\cdot)\) \(\chi_{6003}(2213,\cdot)\) \(\chi_{6003}(2384,\cdot)\) \(\chi_{6003}(2411,\cdot)\) \(\chi_{6003}(2420,\cdot)\) \(\chi_{6003}(2429,\cdot)\) ...

Inducing primitive character

\(\chi_{2001}(80,\cdot)\)

Values on generators

\((668,3133,4555)\) → \((-1,e\left(\frac{9}{22}\right),e\left(\frac{13}{14}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{19}{77}\right)\)\(e\left(\frac{38}{77}\right)\)\(e\left(\frac{26}{77}\right)\)\(e\left(\frac{141}{154}\right)\)\(e\left(\frac{57}{77}\right)\)\(e\left(\frac{45}{77}\right)\)\(e\left(\frac{61}{154}\right)\)\(e\left(\frac{34}{77}\right)\)\(e\left(\frac{25}{154}\right)\)\(e\left(\frac{76}{77}\right)\)
value at  e.g. 2

Related number fields

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