Properties

Conductor 3021
Order 78
Real No
Primitive No
Parity Odd
Orbit Label 6042.cd

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[11]
 
pari: [g,chi] = znchar(Mod(11,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 78
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.cd
Orbit index = 56

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 ]
 

\(\chi_{6042}(11,\cdot)\) \(\chi_{6042}(197,\cdot)\) \(\chi_{6042}(467,\cdot)\) \(\chi_{6042}(539,\cdot)\) \(\chi_{6042}(653,\cdot)\) \(\chi_{6042}(695,\cdot)\) \(\chi_{6042}(767,\cdot)\) \(\chi_{6042}(1151,\cdot)\) \(\chi_{6042}(1223,\cdot)\) \(\chi_{6042}(1493,\cdot)\) \(\chi_{6042}(1607,\cdot)\) \(\chi_{6042}(1721,\cdot)\) \(\chi_{6042}(2021,\cdot)\) \(\chi_{6042}(2177,\cdot)\) \(\chi_{6042}(2975,\cdot)\) \(\chi_{6042}(3845,\cdot)\) \(\chi_{6042}(3959,\cdot)\) \(\chi_{6042}(4757,\cdot)\) \(\chi_{6042}(4799,\cdot)\) \(\chi_{6042}(4913,\cdot)\) \(\chi_{6042}(5099,\cdot)\) \(\chi_{6042}(5555,\cdot)\) \(\chi_{6042}(5711,\cdot)\) \(\chi_{6042}(5783,\cdot)\)

Inducing primitive character

\(\chi_{3021}(11,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{3}{26}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{4}{39}\right)\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{7}{39}\right)\)\(e\left(\frac{11}{78}\right)\)\(e\left(\frac{21}{26}\right)\)\(e\left(\frac{8}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{39})\)