Properties

Conductor 1007
Order 234
Real No
Primitive No
Parity Even
Orbit Label 6042.cn

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[25]
 
pari: [g,chi] = znchar(Mod(25,6042))
 

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 = Even
Orbit label = 6042.cn
Orbit index = 66

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 ]
 

\(\chi_{6042}(25,\cdot)\) \(\chi_{6042}(43,\cdot)\) \(\chi_{6042}(199,\cdot)\) \(\chi_{6042}(271,\cdot)\) \(\chi_{6042}(481,\cdot)\) \(\chi_{6042}(517,\cdot)\) \(\chi_{6042}(541,\cdot)\) \(\chi_{6042}(643,\cdot)\) \(\chi_{6042}(727,\cdot)\) \(\chi_{6042}(859,\cdot)\) \(\chi_{6042}(997,\cdot)\) \(\chi_{6042}(1069,\cdot)\) \(\chi_{6042}(1183,\cdot)\) \(\chi_{6042}(1195,\cdot)\) \(\chi_{6042}(1225,\cdot)\) \(\chi_{6042}(1279,\cdot)\) \(\chi_{6042}(1297,\cdot)\) \(\chi_{6042}(1309,\cdot)\) \(\chi_{6042}(1315,\cdot)\) \(\chi_{6042}(1543,\cdot)\) \(\chi_{6042}(1681,\cdot)\) \(\chi_{6042}(1753,\cdot)\) \(\chi_{6042}(1999,\cdot)\) \(\chi_{6042}(2023,\cdot)\) \(\chi_{6042}(2107,\cdot)\) \(\chi_{6042}(2137,\cdot)\) \(\chi_{6042}(2251,\cdot)\) \(\chi_{6042}(2341,\cdot)\) \(\chi_{6042}(2449,\cdot)\) \(\chi_{6042}(2455,\cdot)\) ...

Inducing primitive character

\(\chi_{1007}(25,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{7}{9}\right),e\left(\frac{21}{26}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{95}{234}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{7}{39}\right)\)\(e\left(\frac{32}{117}\right)\)\(e\left(\frac{100}{117}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{95}{117}\right)\)\(e\left(\frac{44}{117}\right)\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{89}{234}\right)\)
value at  e.g. 2

Related number fields

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