Properties

Conductor 473
Order 35
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.cf

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(4730)
 
sage: chi = H[471]
 
pari: [g,chi] = znchar(Mod(471,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 35
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4730.cf
Orbit index = 58

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 ]
 

\(\chi_{4730}(471,\cdot)\) \(\chi_{4730}(1301,\cdot)\) \(\chi_{4730}(1411,\cdot)\) \(\chi_{4730}(1521,\cdot)\) \(\chi_{4730}(1681,\cdot)\) \(\chi_{4730}(1731,\cdot)\) \(\chi_{4730}(1741,\cdot)\) \(\chi_{4730}(1841,\cdot)\) \(\chi_{4730}(1951,\cdot)\) \(\chi_{4730}(2161,\cdot)\) \(\chi_{4730}(2171,\cdot)\) \(\chi_{4730}(2271,\cdot)\) \(\chi_{4730}(2381,\cdot)\) \(\chi_{4730}(2601,\cdot)\) \(\chi_{4730}(2621,\cdot)\) \(\chi_{4730}(3051,\cdot)\) \(\chi_{4730}(3481,\cdot)\) \(\chi_{4730}(3831,\cdot)\) \(\chi_{4730}(3881,\cdot)\) \(\chi_{4730}(3991,\cdot)\) \(\chi_{4730}(4101,\cdot)\) \(\chi_{4730}(4261,\cdot)\) \(\chi_{4730}(4321,\cdot)\) \(\chi_{4730}(4691,\cdot)\)

Values on generators

\((947,431,1981)\) → \((1,e\left(\frac{3}{5}\right),e\left(\frac{1}{7}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{33}{35}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{6}{35}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{1}{7}\right)\)\(e\left(\frac{2}{7}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{2}{35}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)