Properties

Conductor 1007
Order 26
Real No
Primitive No
Parity Odd
Orbit Label 6042.bl

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[37]
 
pari: [g,chi] = znchar(Mod(37,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 26
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.bl
Orbit index = 38

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 ]
 

\(\chi_{6042}(37,\cdot)\) \(\chi_{6042}(835,\cdot)\) \(\chi_{6042}(1177,\cdot)\) \(\chi_{6042}(1633,\cdot)\) \(\chi_{6042}(1861,\cdot)\) \(\chi_{6042}(2317,\cdot)\) \(\chi_{6042}(2659,\cdot)\) \(\chi_{6042}(2773,\cdot)\) \(\chi_{6042}(2887,\cdot)\) \(\chi_{6042}(3343,\cdot)\) \(\chi_{6042}(4141,\cdot)\) \(\chi_{6042}(5965,\cdot)\)

Inducing primitive character

\(\chi_{1007}(37,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,-1,e\left(\frac{15}{26}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{3}{26}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{9}{26}\right)\)\(e\left(\frac{10}{13}\right)\)\(-1\)\(e\left(\frac{3}{13}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{5}{26}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{13})\)