Properties

Conductor 1007
Order 234
Real No
Primitive No
Parity Odd
Orbit Label 6042.co

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(6042)
 
sage: chi = H[13]
 
pari: [g,chi] = znchar(Mod(13,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 234
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 = Odd
Orbit label = 6042.co
Orbit index = 67

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 ]
 

\(\chi_{6042}(13,\cdot)\) \(\chi_{6042}(97,\cdot)\) \(\chi_{6042}(205,\cdot)\) \(\chi_{6042}(307,\cdot)\) \(\chi_{6042}(439,\cdot)\) \(\chi_{6042}(523,\cdot)\) \(\chi_{6042}(649,\cdot)\) \(\chi_{6042}(811,\cdot)\) \(\chi_{6042}(895,\cdot)\) \(\chi_{6042}(925,\cdot)\) \(\chi_{6042}(1003,\cdot)\) \(\chi_{6042}(1123,\cdot)\) \(\chi_{6042}(1321,\cdot)\) \(\chi_{6042}(1447,\cdot)\) \(\chi_{6042}(1459,\cdot)\) \(\chi_{6042}(1477,\cdot)\) \(\chi_{6042}(1561,\cdot)\) \(\chi_{6042}(1573,\cdot)\) \(\chi_{6042}(1579,\cdot)\) \(\chi_{6042}(1687,\cdot)\) \(\chi_{6042}(1777,\cdot)\) \(\chi_{6042}(1891,\cdot)\) \(\chi_{6042}(1921,\cdot)\) \(\chi_{6042}(2005,\cdot)\) \(\chi_{6042}(2029,\cdot)\) \(\chi_{6042}(2275,\cdot)\) \(\chi_{6042}(2347,\cdot)\) \(\chi_{6042}(2485,\cdot)\) \(\chi_{6042}(2713,\cdot)\) \(\chi_{6042}(2719,\cdot)\) ...

Inducing primitive character

\(\chi_{1007}(13,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{5}{18}\right),e\left(\frac{6}{13}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{16}{117}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{4}{39}\right)\)\(e\left(\frac{109}{234}\right)\)\(e\left(\frac{46}{117}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{32}{117}\right)\)\(e\left(\frac{223}{234}\right)\)\(e\left(\frac{31}{78}\right)\)\(e\left(\frac{31}{117}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{117})\)