Properties

Conductor 2365
Order 70
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.cx

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[39]
 
pari: [g,chi] = znchar(Mod(39,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2365
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 70
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.cx
Orbit index = 76

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 ]
 

\(\chi_{4730}(39,\cdot)\) \(\chi_{4730}(409,\cdot)\) \(\chi_{4730}(469,\cdot)\) \(\chi_{4730}(629,\cdot)\) \(\chi_{4730}(739,\cdot)\) \(\chi_{4730}(849,\cdot)\) \(\chi_{4730}(899,\cdot)\) \(\chi_{4730}(1249,\cdot)\) \(\chi_{4730}(1679,\cdot)\) \(\chi_{4730}(2109,\cdot)\) \(\chi_{4730}(2129,\cdot)\) \(\chi_{4730}(2349,\cdot)\) \(\chi_{4730}(2459,\cdot)\) \(\chi_{4730}(2559,\cdot)\) \(\chi_{4730}(2569,\cdot)\) \(\chi_{4730}(2779,\cdot)\) \(\chi_{4730}(2889,\cdot)\) \(\chi_{4730}(2989,\cdot)\) \(\chi_{4730}(2999,\cdot)\) \(\chi_{4730}(3049,\cdot)\) \(\chi_{4730}(3209,\cdot)\) \(\chi_{4730}(3319,\cdot)\) \(\chi_{4730}(3429,\cdot)\) \(\chi_{4730}(4259,\cdot)\)

Values on generators

\((947,431,1981)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{11}{14}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{19}{35}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{22}{35}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{18}{35}\right)\)
value at  e.g. 2

Related number fields

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