Properties

Conductor 945
Order 36
Real No
Primitive No
Parity Even
Orbit Label 9450.fa

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(9450)
 
sage: chi = H[643]
 
pari: [g,chi] = znchar(Mod(643,9450))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 945
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 36
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 = 9450.fa
Orbit index = 131

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 ]
 

\(\chi_{9450}(643,\cdot)\) \(\chi_{9450}(1357,\cdot)\) \(\chi_{9450}(2407,\cdot)\) \(\chi_{9450}(2743,\cdot)\) \(\chi_{9450}(3793,\cdot)\) \(\chi_{9450}(4507,\cdot)\) \(\chi_{9450}(5557,\cdot)\) \(\chi_{9450}(5893,\cdot)\) \(\chi_{9450}(6943,\cdot)\) \(\chi_{9450}(7657,\cdot)\) \(\chi_{9450}(8707,\cdot)\) \(\chi_{9450}(9043,\cdot)\)

Inducing primitive character

\(\chi_{945}(643,\cdot)\)

Values on generators

\((9101,6427,6751)\) → \((e\left(\frac{7}{9}\right),-i,-1)\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{35}{36}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{13}{36}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{36})\)