Properties

Conductor 2009
Order 105
Real No
Primitive No
Parity Even
Orbit Label 6027.ds

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(6027)
 
sage: chi = H[16]
 
pari: [g,chi] = znchar(Mod(16,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 105
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 = 6027.ds
Orbit index = 97

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 ]
 

\(\chi_{6027}(16,\cdot)\) \(\chi_{6027}(37,\cdot)\) \(\chi_{6027}(100,\cdot)\) \(\chi_{6027}(256,\cdot)\) \(\chi_{6027}(529,\cdot)\) \(\chi_{6027}(592,\cdot)\) \(\chi_{6027}(625,\cdot)\) \(\chi_{6027}(877,\cdot)\) \(\chi_{6027}(898,\cdot)\) \(\chi_{6027}(1117,\cdot)\) \(\chi_{6027}(1369,\cdot)\) \(\chi_{6027}(1453,\cdot)\) \(\chi_{6027}(1486,\cdot)\) \(\chi_{6027}(1738,\cdot)\) \(\chi_{6027}(1759,\cdot)\) \(\chi_{6027}(1822,\cdot)\) \(\chi_{6027}(2230,\cdot)\) \(\chi_{6027}(2251,\cdot)\) \(\chi_{6027}(2314,\cdot)\) \(\chi_{6027}(2347,\cdot)\) \(\chi_{6027}(2599,\cdot)\) \(\chi_{6027}(2620,\cdot)\) \(\chi_{6027}(2683,\cdot)\) \(\chi_{6027}(2839,\cdot)\) \(\chi_{6027}(3091,\cdot)\) \(\chi_{6027}(3112,\cdot)\) \(\chi_{6027}(3175,\cdot)\) \(\chi_{6027}(3208,\cdot)\) \(\chi_{6027}(3481,\cdot)\) \(\chi_{6027}(3544,\cdot)\) ...

Inducing primitive character

\(\chi_{2009}(16,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{10}{21}\right),e\left(\frac{3}{5}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{103}{105}\right)\)\(e\left(\frac{101}{105}\right)\)\(e\left(\frac{1}{105}\right)\)\(e\left(\frac{33}{35}\right)\)\(e\left(\frac{104}{105}\right)\)\(e\left(\frac{89}{105}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{97}{105}\right)\)\(e\left(\frac{74}{105}\right)\)\(e\left(\frac{1}{15}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)